NewLifeCA Back Issues

[dvgrn]

NewLifeCA #24, 9/9/2022 9:31pm

NewLifeCA#24, 9 September 2022: Oscillator Overload and Miscellaneous Mechanisms

This post will contain relatively few actual patterns, but not because discoveries have slowed down at all in the last couple of months -- quite the opposite.

Oscillators
There have been so many discoveries in the high-period oscillator department that the only way to summarize them is in a stamp collection.

These are just the 100+ new oscillators that have been discovered since the last NewLifeCA message on July 9th -- or most of them, at least.  A few more may be present in the larger collection, but not labeled well enough yet to be picked out with a search by date.  Larger collections including (almost) all of the new oscillators found in 2022 can be seen in posts surrounding the one above.

Many of these can now be found in the various LifeWiki "hassler" category pages linked to in the previous message.  More are still showing up, just about every day.  The hassler discoveries fairly regularly improve on the size or population records for their periods, and occasionally enable new small guns.

A few of the new appearances are soup search results rather than engineered spark-supported hasslers; examples include the surprising new p7 meatball-type symmetric sparker and p11 thumb sparker found by Charity Engine on August 2 and August 11, respectively.

A byproduct of the "hassler" oscillator searches is that it's always possible that a pattern will repeat at one of the remaining missing periods, p19 or p41 -- *and* (rather unlikely but possible) the supporting sparks will turn out to be replaceable by some stable catalyst, or by a blinker that is rephased by the active reaction.  Some other lines of research that might lead to a proof of Life omniperiodicity are also being pursued, but these oscillator searches seem to be getting the most attention at the moment.

However, oscillators aren't the only game in town, although they're certainly far ahead on sheer volume.  

Glider Syntheses
New glider syntheses are still being regularly found and improved upon, with the improvements reported to the Catagolue "Syntheses" page.. On July 15th the work was completed to show that all strict still lifes with 14 or fewer bits can be constructed in at most 9 gliders.

The similar "15-in-10" project is still in progress; completing it needs just a one-glider cost improvement in a single-digit number of recipes.

On August 16th, EvinZL completed an "octo3g" orientation-agnostic hash library for the existing database of 3-glider collisions. This allows active 3G collision patterns to be searched in the same way as active patterns in the previous octo3obj and octohash databases. The search script reliably finds all exact pattern matches fairly quickly, without the sometimes crippling levels of false positives that the previous population-sequence searches could produce.

Conduits and Converters
Signal circuitry has been getting quite a bit of attention, partly with boosts from new gun or reflector mechanisms made possible by oscillator discoveries.  For example, a periodic "bumper" reflector was finally found with the minimum possible period of 34, using the new p34 from early July.

On July 24th Tanner Jacobi improved on his previous G-to-H conduit from seven years ago, with a new "speed tunnel" mechanism that recovers in only 61 ticks instead of the syringe's 74/75/78+ ticks.

Code: Select all

#C https://conwaylife.com/wiki/Speed_tunnel
x = 48, y = 31, rule = B3/S23
15b2ob2o$16bobo$11b2obo5bob2o$10bobob2o3b2obobo$9bo6bobo6bo$2bo6b7o3b
7o$obo$b2o8b3o7b3o$10bo2bo3bo3bo2bo$10b2o4bobo4b2o21bo$16bobo26bobo$
17bo27bobo$46bo$35bo$35bo$24b2o9b3o$24b2o11bo4$6b2o$6bobo19b2o$8bo6b2o
5b2o5bo$8b3o3bo2bo4bobob3o$6b2o3bo3bobo6bobo$5bo2b4o4bo7b2o$5b2obo10b
2o$8bob2o7bo$8bobo9b3o$7b2obobo9bo$11b2o!

Much more recently, iNoMed has used a period-68 gun mechanism to bring the size of a pseudo-p17 gun down to 164x158, with every indication that it will continue to shrink.  Paul Chapman's original pseudo-p17 gun (from 6 April 2003) was 494x368. so the reduction in area is now just over a factor of seven.

And two new Herschel conduits were found today -- a Spartan L224 by Tanner Jacobi, and a record-breaking fastest known (I think) stable Rx conduit by affamatodidio.  It's an Rx113 using a stable reflector found by Simon Ekström on July 25 (which is a variation on the speed tunnel):

Code: Select all

#C syringe + Fx77 + new Rx113, repeat time 182,
#C followed by syringe + Fx153 + new L224, repeat time 292 (shown)
#C The repeat time for the R113 has since been reduced to 170, as shown in
#C https://conwaylife.com/forums/viewtopic.php?p=150815#p150815
x = 259, y = 124, rule = B3/S23
235b2o$234bo2bo$235b2o12$254bo$252b3o$251bo$251b2o$257b2o$257bo$169b2o
11bo72bobo$169b2o10bobo71b2o$181bobo2b2o3bo$180b2ob2o2bo2bobo$80b2o11b
o90bobo3bobo$80b2o10bobo85b2obo2b4obo3bo9bo$92bobo2b2o3bo77b2obobo3bo
5b3o5b3o$91b2ob2o2bo2bobo12bo67bobo3bo7bo3bo16bo$95bobo3bobo10b3o68bob
o3bo5b2o3b2o13b3o$91b2obo2b4obo10bo72bo3b2o24bo$91b2obobo3bo12b2o101b
2o$95bobo3bo$96bobo3bo$97bo3b2o27bo46b2o$129bobo45b2o$129bobo30b2o$
130bo30bo2bo54b2o$88b2o54b2o14bob2o55b2o$88b2o54bo15bo94b2o$73b2o67bob
o14b2o94b2o$72bo2bo66b2o30b2o$71bob2o72bo26bo$71bo73b3o27b3o$70b2o72bo
32bo10b2o$85b2o55bo2bo41bobo11b2o6bo28b2o$85bo56b4o41bo13b2o6b3o26b2o
5b2o$86b3o24b2o71b2o24bo33bo$88bo11b2o11b2o27b2o67b2o30b3o$73b3o25bo
41bo99bo$75bo19b2ob3o42bobo$74bo21bobo45b2o$94bobobo13bo$94b2o3b2o9b3o
12bob2o$100bo8bo15b2obo$97b3o3bo5b2o$96bo3b4o30b2o$96bobo35b2o$97b2ob
2o$100b2o$97b2o$97bo$98bo$97b2o$115b2o$114bobo$99b2o5b2o6bo$98bobo4bo
2bo3b3o$98bo6bobo3bo3b2o$97b2o7bo4b4o2bo$102b2o10bob2o$103bo7b2obo$
100b3o9bobo$100bo9bobob2o$110b2o9$131b2o$130bo2bo$131b2o37$3o$2bo$bo!

Quite a few other elementary signal conduits have turned up recently, notably Mitchell Riley's H-to-R conduit from July 14th, which has an astonishingly low repeat time of only 57 ticks while still releasing an output glider.

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #25, 9/12/2022 2:42pm

NewLifeCA #25, 12 September 2022: new p38 and p43 and p168, H-to-Gs, and minor RCT progress

Three days ago Nico Brown turned up another nontrivial period-38 oscillator, this one with eightfold symmetry making use of the old glider-block cycle reaction:

Code: Select all

#N Nico's p38 / 232P38
#O Nico Brown, 9/9/2022
#C p38 honeyfarm hassler with eightfold symmetry
#C https://conwaylife.com/forums/viewtopic.php?p=150828#p150828
x = 58, y = 58, rule = B3/S23
19b2o16b2o$19b2o16b2o3$9b2o36b2o$10bo36bo$10bobo15b2o15bobo$11b2o15b2o
15b2o2$4bo14b3o14b3o14bo$4b3o12bobo14bobo12b3o$7bo10bo2bo14bo2bo10bo$
6b2o11b2o16b2o11b2o3$22b2o10b2o$22bo12bo$23b3o6b3o$11bo13bo6bo13bo$2o
7b2obo32bob2o7b2o$2o7bo2bo32bo2bo7b2o$9b3o34b3o$15b2o24b2o$15bobo22bob
o$17bo22bo$17b2o20b2o3$6b2o42b2o$6b2o42b2o3$17b2o20b2o$17bo22bo$15bobo
22bobo$15b2o24b2o$9b3o34b3o$2o7bo2bo32bo2bo7b2o$2o7b2obo32bob2o7b2o$
11bo13bo6bo13bo$23b3o6b3o$22bo12bo$22b2o10b2o3$6b2o11b2o16b2o11b2o$7bo
10bo2bo14bo2bo10bo$4b3o12bobo14bobo12b3o$4bo14b3o14b3o14bo2$11b2o15b2o
15b2o$10bobo15b2o15bobo$10bo36bo$9b2o36b2o3$19b2o16b2o$19b2o16b2o!

I think this is the fourth known completed p38 engine, if you count the period-specific mechanisms that were found to be supportable by Raucci's p38 (see here and here).

Yesterday the second known p43 oscillator mechanism showed up, also found by Nico Brown -- the first engine not reliant on a signal loop. This one is actually an impressively small glider gun:

Code: Select all

#N p43 gun
#O Nico Brown, 9/11/2022
#C https://conwaylife.com/forums/viewtopic.php?p=150883#p150883
x = 32, y = 25, rule = B3/S23
10b2o$2b2o6bobob2o$3bo8bobobo7bo$3bobo5bo2bo2bo5bobo$4b2o5b2o2b2o7bo3$
2o$bo$bobo19bo$2b2o4b2o13bo$9bo13bo2$8bo13bo$8bo13b2o4b2o$8bo19bobo$
30bo$30b2o3$7bo7b2o2b2o$6bobo5bo2bo2bo$7bo7bobobo7bobo$16b2obobo6b2o$
20b2o6bo!

People on Discord are currently working out the implications for reducing various multiple-of-43 glider gun periods, using the usual variety of period-multiplication mechanisms.

The p38 and p43 would both have been much more exciting if they'd been found a year or a decade ago, before their respective same-period predecessors. But it's still very interesting that discoveries like this are showing up so regularly these days, where only stable supports are needed instead of periodic sparks.

There seems to be a lot of unexplored search space within reach of Mitchell Riley's symmetric CatForce program and other custom oscillator search programs that are getting exercised these days. For anyone interested in a deeper dive, for example, the README for Luke Kiernan's GitHub repo might be worth reviewing.

These high-period oscillator searches aren't targeted to any particular period, so any period *could* show up, including the two remaining missing periods 19 and 41. Of course some obscure corollary of Murphy's Law will probably guarantee that we find at least two or three oscillators of every other possible period, before a p19 and a p41 finally show up. But every new discovery is at least showing that these searches are being run in interesting new territory.

Oscillators Compounded Daily
The rush of new oscillator discoveries also keeps making available more and more potential tools to solve other partials -- "partials" being the incomplete patterns that search programs like David Raucci's have been producing in great profusion for the last year and change. There's a known set of sparks for each partial that will turn it into a working oscillator, so the problem for each case is to find something that will supply that spark (or a workable substitute). Of course that's a very tall order for a lot of prime periods, let alone p19 or p41, but there are lots of composite-period partials where some inspired engineering can produce good results.

Today, for example, a tricky period-168 oscillator was completed, using previously discovered lower-period hasslers to supply the supporting sparks for the p168 mechanism. It's labeled as an R-pentomino hassler, but it could equally well be classed as a B-heptomino hassler, and there's even a queen-bee stage for a while:

Code: Select all

#N p168 R-pentomino hassler
#O iNoMed, 12 September 2022
#C This is an R/B/QB hassler based on a partial by David Raucci
#C https://conwaylife.com/forums/viewtopic.php?p=150904#p150904
x = 69, y = 59, rule = B3/S23
36bo$34b3o$33bo$5b2o26b2o$6bo$6bobo16b2o$7b2o15b2o17b2o$23bob2o14bo2bo
$24bo2$41b2obo$20bo22bobo2b2o$18b2obo22bo4bo$19b2o15b2o7bo$18b2o16bobo
6bo2bo$38bo$10b2o26b2o13bo$11bo40bo$8b3o42b2ob2o$8bo43bo4bo$51b3ob3o$
51bo4bo$51b2ob2o$56bo$55bo$bo2bo31b3o23b2o$4bo31bo23bo2bo$o4bo30bo$2o
2bobo30b2obo$5bob2o18b2o11b2o18b2obo$28bob2o30bobo2b2o$32bo30bo4bo$5bo
2bo23bo31bo$5b2o23b3o31bo2bo$13bo$12bo$13b2ob2o$12bo4bo$11b3ob3o$11bo
4bo43bo$11b2ob2o42b3o$16bo40bo$15bo13b2o26b2o$30bo$20bo2bo6bobo16b2o$
23bo7b2o15b2o$19bo4bo22bob2o$19b2o2bobo22bo$24bob2o2$44bo$24bo2bo14b2o
bo$24b2o17b2o15b2o$42b2o16bobo$62bo$34b2o26b2o$35bo$32b3o$32bo!

H-to-Gs
Just to mention in passing: the CatForce search by Tanner Jacobi that turned up the L224 Herschel conduit (see NewLifeCA #24), also produced a good number of new Herschel-to-glider converters.

Some hundreds of these have now been collected and catalogued in that forum thread. It's gradually becoming more and more likely that, when a specific output glider timing is needed to make an efficient connection in a larger construction, exactly the right H-to-G will turn out to be available in the collection. Over time, new H-to-Gs also tend to gradually shrink the average size of the guns in the glider gun collection.

RCT progress
The project of producing a complete model RCT pattern, showing how a 16-glider recipe can produce any structure that can be constructed with any number of gliders, has been moving along rather slowly for the last few months. But it's still moving, and the number of remaining unsolved pieces is looking fairly manageable.

Here, for example, is a LifeViewer animation of the slow salvo that will clean up all of the GPSE ash to the southwest that is created by the "divide by two and take the remainder" RCT bit-reading mechanism. In a real RCT pattern there will be a ridiculously long line of GPSE ash between the Cordership creation points and the Corderabsorbers in the far southwest. Similar slow salvos are being compiled to build the somewhat larger NW and SE Corderfleets.

After that, one of the next unfinished jobs is to build a "slow^2 salvo" compiler -- a script that takes a slow-salvo list of lanes as input, and produces a new slow salvo aimed at a block that emits that specific input slow salvo at 90 degrees. This will be needed for some of the remaining construction tasks in the far corners. For example, a slow^2 salvo will build the Corderabsorbers shown in the LifeViewer animation above, a safe distance behind the SW GPSE ash trails.

Anyone interested in helping out with any of these remaining RCT coding tasks can post something here.

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #26, 10/8/2022 8:56am

NewLifeCA #26, 8 October 2022: The Hunt for New Patterns in October

October came in with a bang this year, and I don't want this month to get away without a NewLifeCA mention of the October surge.  I'm short of time and don't have a whole lot to add to what's currently in the Current News pane on LifeWiki -- but it won't stay on the front page forever, so I'll just quickly reproduce the list here:

• October 1[/b]: Luke Kiernan and iNoMed discover the p68 pi-heptomino hassler, the smallest known period-68 oscillator.
• October 1: Nico Brown discovers 115P106, the smallest known period-106 oscillator.
• October 2: Mitchell Riley finds a third period-23 oscillator engine, 92P23, a beehive-and-honeyfarm hassler.
• October 2: Charity Engine discovers a small p28 block puffer using apgsearch.
• October 2: cvojan and vivi discover a period-24 glider gun with a 21x20 bounding box, later reduced to 20x20 by James Pascua, making it the second smallest known glider gun with a unique period.
• October 2: Using parts of a new extensible 8-engine Cordership, Brett Berger completes a pattern that produces a single glider stream with an irrational bit density, followed by another pattern that emits gliders in a line whose slope is the golden ratio.
• October 3: The Open Science Grid discovers 76P86, the smallest known period-86 oscillator, using apgsearch.
• October 3: cvojan and iNoMed discover a period-40 glider gun with a 27x20 bounding box - the fourth smallest glider gun with a unique period.
• October 3: Mitchell Riley and iNoMed discover 52P44, the smallest non-LCM based period-44 oscillator.

These kinds of discoveries tend to build on each other, slowly but surely, as new oscillators produce new types of edge sparks that can then be used to support other oscillators of the same period.

One of the big drivers of interest in these new oscillators seems to be the ConwayLife Lounge server on Discord, plus Jeremy Tan's "Skopje" project -- a database separate from the updated oscillator collection (in Golly and on Github) and the gun and truegun collections (on Catagolue) which are, respectively, the several-generations descendants of Dean Hickerson's oscillator stamp collection and of Jason Summers' curated copy of Dieter and Peter's gun collection, both dating from the mid-1990s.

As mentioned back on June 2, Skopje collects the Smallest Known Oscillators of Population {n}, "SKOPn". There's also some focus on finding glider syntheses of these oscillators whenever possible.

The primary area of interest is oscillators up to period 187 or so, above which an oscillator of any period can be trivially constructed with exactly 141 live cells -- and above p106, any non-multiple of four can be produced by a rectifier loop with no more than 156 live cells, and so on.  New high-period discoveries have to beat those baselines at a minimum, and also beat any previous period-specific discoveries.

Skopje provides a useful way to measure the "interestingness" of new discoveries.  If an oscillator produces a new smallest-population record at a given period, that's generally a sign that it's interesting -- and probably notable, in the sense that no one is likely to object to a new Skopje record-holder getting a mention in the LifeWiki.

Of course new records at any period are progressively more difficult to find as more discoveries are made.  This has spurred the development of some new search engines and variants of old ones, such as symmetric CatForce.

The algorithms used to search for these new oscillators mostly amount to a roll of the dice, as far as period is concerned.  Most of these periods are far too large to allow for a direct search at that specific period, so we're getting whatever happens to show up -- a search script tries a lot of relative positionings of active reactions and catalysts, and flags the ones where the active reactions happen to reappear after any number of ticks.

One big hope is that if our patience holds out and we roll the dice often enough, a partial will appear that matches one of the remaining missing periods (p19 and p41) and that can be completed with stable catalysts. There have been a lot of near misses, in various senses. For example, if the sparks to the left and right in the patterns below could be replaced with some kind of custom catalyst, the result would be a p19 oscillator and a p41 oscillator, respectively (Discord links):

Code: Select all

#N p19 partial
#O Carson Cheng, 10/7/2022

x = 24, y = 10, rule = B3/S23
b2o18b2o$4o16b4o$4o3bo8bo3b4o$4o2b2o3b2o3b2o2b4o$4ob2o10b2ob4o$b2o3b2o
2bo2bo2b2o3b2o$7bob2o2b2obo$9b2o2b2o$11b2o$11b2o!

Code: Select all

#N p41 partial
#O Carson Cheng, 10/7/2022
#C (sample spark is a part of Rich's p16)

x = 36, y = 18, rule = B3/S23
4b2o24b2o$4bobo2b2o14b2o2bobo$bo4bo3bo14bo3bo4bo$b5ob3o16b3ob5o$5bobo
20bobo$b3obobo20bobob3o$o2bob2o22b2obo2bo$2o11b2o6b2o11b2o$13bobo4bobo
$14bo6bo$17b2o$3bo3b3o2b3o6b3o2b3o3bo$2b3o12b2o12b3o$bobobo8bo6bo8bobo
bo$bobob2o6bobo4bobo6b2obobo$b4obo6b2o6b2o6bob4o$2b5o22b5o$3bo28bo!

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #26 forwarded responses, 8 October 2022 8:49pm

It often happens that something new and interesting shows up as soon as I click Send on one of these NewLifeCA messages, requiring an addendum.

• October 8: Charity Engine discovers 34P20, the smallest known non-LCM-based period-20 oscillator. It is also the first known period-20 oscillator with volatility 1, although it is not strictly volatile.

Code: Select all

#N 34P20
#O Charity Engine, 8 October 2022
x = 14, y = 14, rule = B3/S23
4b2o$4b2o3$2o3bo$2o2bobo2b3o$5bo3bo2bo$8bo3bo$7bobo3bo$5b2obobobo$5bo
3bo$5bo$6b2obo$8bo!

It seems a bit surprising that this oscillator hasn't showed up before, somehow.  Also it's only one tick away from being a period-19 oscillator -- though I may be taken to task by some people for saying that, since it's a mod 10 flipper, therefore unavoidably even-period, really nowhere near being a counterfactual almost-p19.

Code: Select all

#N 23-glider synthesis of 34P20
#O Tanner Jacobi, 8 October 2022
#C https://discord.com/channels/357922255553953794/370571014654001154/1028359066466131968
x = 214, y = 47, rule = B3/S23
194bo$193bo$193b3o3$190bobo$191b2o$191bo$184bo25bo$185b2o22bo$184b2o
23b3o3$179bobo$180b2o$180bo4$176bo$177b2o$125bo50b2o$8bobo113bobo45b2o
23bo$9b2o3bo50bo9bo48bo2bo43bobo22bobo$9bo3bo50bobo8bobo44b2obobo45bo
22bo2bo$13b3o48bo2bo7b2o44bo2bobo67b2obobo$62b2obobo54bo2bo67bo2bobo$
61bo2bobo8bo47b2o3bo4bo60bo2bo$62bo2bo8b2o51bobo3bobo59b2o3bo$63b2o9bo
bo51bo4b2o64bobo2b2o5b2o$o135b2o62bo3b2o5bobo$b2o133bobo72bo$2o134bo$
127b3o70b2o$129bo70b2o$2b2o124bo$bobo18b3o52bo52b3o$3bo18bo53b2o52bo$
23bo52bobo52bo48b2o$179bobo$181bo18b3o$200bo$201bo2$14b2o$14bobo$14bo!

EDIT: Slight optimization by Carson Cheng, not big enough to merit another email but I can sneak it in here:

Code: Select all

#N 22-glider synthesis of 34P20
#O Tanner Jacobi and Carson Cheng, 8 October 2022
#C https://discord.com/channels/357922255553953794/370571014654001154/1028359066466131968
#C https://discord.com/channels/357922255553953794/370571014654001154/1028481393346494464
x = 214, y = 47, rule = B3/S23
194bo$193bo$193b3o3$190bobo$191b2o$191bo$184bo25bo$185b2o22bo$184b2o
23b3o3$179bobo$180b2o$180bo4$176bo$177b2o$125bo50b2o$8bobo113bobo45b2o
23bo$9b2o3bo50bo58bo2bo43bobo22bobo$9bo3bo50bobo55b2obobo45bo22bo2bo$
13b3o48bo2bo53bo2bobo67b2obobo$62b2obobo54bo2bo67bo2bobo$61bo2bobo56b
2o3bo65bo2bo$62bo2bo61bobo2b2o61b2o3bo$63b2o63bo3b2o65bobo2b2o5b2o$o
199bo3b2o5bobo$b2o208bo$2o$69bo57b2o71b2o$69b2o55bobo71b2o$2b2o64bobo
57bo$bobo18b3o106b2o$3bo18bo52b2o54bobo$23bo51bobo53bo48b2o$75bo103bob
o$59bo121bo18b3o$59b2o18b2o119bo$58bobo18bobo119bo$79bo$14b2o$14bobo$
14bo!

Dave, this feels like a bad case of the stupids, but where are these two "irrational" patterns?  Somehow in waterbear??

Sorry, that was my mistake -- I skimped a bit on transcribing the links.  Links are much more thorough in the CurrentNews pane on LifeWiki, so it's generally worth looking there whenever puzzling cases like this show up.

Dean Hickerson wrote, as if in response but a couple of hours before:

October 2: Using parts of a new extensible 8-engine Cordership, Brett Berger completes a pattern that produces a single glider stream with an irrational bit density, followed by another pattern that emits gliders in a line whose slope is the golden ratio.

That link shows the 8-engine Cordership, but not the irrational patterns.  I searched on conwaylife.com and found a correct reference. And here's a description on the LifeWiki.

I built some smaller irrational density patterns back in the 1990s, using *LWSS puffers instead of Corderships.  They can be found at:

    https://conwaylife.com/ref/DRH/irrat.lin.html

In particular, the "p60 version of Irrational 5" produces a glider stream with density  (3 - sqrt(5))/2  relative to a complete p120 glider stream:

Code: Select all

#N p60 version of Irrational 5
#C Two puffers move east, producing a westward MWSS and a boat
#C every 60 gens.  Two stationary guns produce a glider every 60
#C gens and an eastward MWSS every 120 gens; half of the gliders
#C delete the MWSSs while the other half escape.  But when a
#C westward MWSS reaches the guns, it deletes 2 consecutive gliders,
#C allowing one eastward MWSS to escape and suppressing one output
#C glider.  When an eastward MWSS hits a boat, it becomes a NEward
#C glider which deletes one westward MWSS.  Thus, each westward
#C MWSS that reaches the guns causes the deletion of a later
#C westward MWSS.  Specifically, if the westward MWSSs are
#C numbered starting at 3, then, for each integer  K >= 2,  MWSS
#C number  floor(K phi)  causes the deletion of MWSS number
#C floor(K (phi+1)),  where  phi = (1 + sqrt(5))/2.  Also, a glider
#C escapes from the bottom of the pattern about generation
#C 120 floor(K (phi+1)).  Relative to a complete p120 glider stream,
#C the resulting stream of gliders has density  1/(phi+1) =
#C (3 - sqrt(5))/2 ~ 0.381966.
#O Dean Hickerson, dean.hickerson@yahoo.com (1/2/99)
x = 151, y = 91, rule = B3/S23
105b2o$103b2ob2o13b2o$103b4o13b4o$104b2o14b2ob2o$122b2o4$119b2o$113b3o
3bobo$92bo17b3o6bob2o$33bo59b2o15bo9b2o$32bobo57b2o16b3o7bo$15b2o15b2o
bo$15bobo14b2ob2o3b2o39b2o$6bo11bo13b2obo5bo36b3ob2o37b2o$6b2o7bo2bo
13bobo43b5o29b4o4b4o7b2o$18bo14bo45b3o25bo3bo3bo4b2ob2o4b2ob2o13b2o$
15bobo90bo6bo6b2o5b4o13b4o$15b2o87bo3bo5bo15b2o14b2ob2o$105b4o39b2o$
100b3o$98b2ob2o$100b3o18bo$34bo70b4o13b2o$35bo41bo26bo3bo12b2o23b2o$
33b3o42b2o28bo38b2o$12bobo62b2o28bo38b2o$10bo3bo101bo29bo$3b2o5bo15b2o
89b2o$3bo5bo16bo2bo86b2o$10bo19bo116b2o$10bo3bo15bo107b4o4b4o$12bobo
15bo99bo6bo3bo4b2ob2o$26bo2bo6b2o93bo9bo6b2o$26b2o8bobo88bo3bo8bo$38bo
89b4o$38b2o83b3o$30b2o68b3o18b2ob2o$30bo2bo65bobob2o18b3o$16bobo15bo6b
2o56bo3bobo22b4o$14bo3bo15bo7bo56bobo3bo21bo3bo$14bo19bo65b2obobo25bo$
7bo5bo16bo2bo68b3o25bo$7b2o5bo15b2o22b4o$14bo3bo34b6o$16bobo34b4ob2o$
57b2o57bo$117bo$51bo14b2o45bo3bo$49b3o10b4ob2o15b4o26b4o$48bo13b6o15bo
3bo21b3o$48b2o13b4o20bo19b2ob2o$86bo22b3o13b2o8bo$114b4o6b4o8bo$113bo
3bo6b2ob2o3bo3bo$68b2o28b2o17bo8b2o5b4o$68bobo27bobo15bo$9b2o23b2o33bo
29bo$9bobo22bo$2o10bo14bo4bobo70b2o17b2o$o8bo2bo13bobo3b2o70bobo16b2o
7b3o$12bo13b2obo76bo17bo2bo6bo$9bobo14b2ob2o94bo6bobo$9b2o15b2obo97b2o
3b2o$26bobo81b2o$27bo19b2o60bobo$47bo63bo23bo$136bo$132bo3bo$48bo67b4o
13b4o$17b2o27bob2o65bo3bo$17bobo26bo72bo$8b2o10bo14bo10bo71bo$8bo8bo2b
o13bobo9bo2bo$20bo13b2obo9b2o$17bobo14b2ob2o4bo$17b2o15b2obo4b2o$34bob
o$35bo31b2o9b2o$66b2o9bobo$61bo6bo7b3o$38bo21bobo12b3o$37bobo18b2o3bo
12b3o$37b2obo8bobo6b2o3bo13bobo5b2o$25b2o10b2ob2o6bo2bo6b2o3bo14b2o5bo
bo$25bo11b2obo6b2o6b2o3bobo24bo$37bobo5b2o3bo3bo2bo3bo25b2o$38bo8b2o6b
2o$48bo2bo$49bobo!

I guess I should post this to the forum.

Dean Hickerson

I just saw @dvgrn 's latest digest email and I wonder where is the best place to reply, either on the original thread or here? I don't have anything to add, just the comment that the small p24 glider gun is really nice and I wonder if anyone has worked on a glider synthesis for it.

The p6 part might be hard. (I am far behind times on what's possible.)

Here is good. The NewLifeCA discussion thread on the forums is also good.

Very weirdly, the synthesis is actually so easy that I could walk into the local Life hardware store and assemble a working p24 gun from pieces right off the shelf.

I'm not very good at syntheses, so it's relatively rare that I get to complete something like this (because there's usually a tricky bit that I don't know how to handle right... either that or someone else does it almost instantly).

So at the moment there's an 18G synthesis, which is represented by a 20G synthesis of a capped version on Catagolue.

Code: Select all

#C 18-glider synthesis of p24 gun
x = 302, y = 40, rule = B3/S23
280bo$278bobo$279b2o3$288bo$282bobo3bobo$283b2o3b2o$283bo$293bobo$238b
obo52b2o$233bo4b2o54bo$234b2o3bo$233b2o$194bo86bo$143bo51b2o85bo14bo2b
o$144bo49b2o45b2o37b3o14bo$142b3o44bo50bo2bo2b2o48bo4bo$147bobo40b2o
48bo2bo2b2o47bobo2b2o$147b2o40b2o3b2o45b2o50b2obo$148bo45bobo$89bo106b
o$87bobo106b2o43b2o50bo2bo$88b2o151b2o52b2o$49bo42bo$50bo41bobo$48b3o
41b2o42b2o47b2o46b2o52b2o$53bobo80b2o47b2o46b2o52b2o$53b2o42b2o43b2o
47b2o46b2o52b2o$54bo42bobo42bobo46bobo45bobo51bobo$bo97bo44bo48bo47bo
53bo$2bo96b2o43b2o47b2o46b2o52b2o$3o5bo33bo45bo44bo48bo101bo$7b2o31bo
2bo42bo2bo41bo2bo45bo2bo45b3o50bo2bo$7bobo30bo2bo42bo2bo41bo2bo45bo2bo
44b3o51bo2bo$41bo45bo44bo48bo101bo$3b3o185b2o$3bo187bobo$4bo188bo$193b
2o!

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #27, 11/7/2022 2:07pm

NewLifeCA #27, 7 November 2022: Uncooperative Oscillator Periods, plus RCT

Oscillators Of Outsized Orneriness

There's been a continued attempt to discover new oscillator periods, with most discussion happening on the ConwayLife Lounge server on Discord.

A primary focus of this effort is to try to turn up oscillators with the two remaining missing periods, p19 and p41 -- more or less by repeatedly rolling the dice, since there's a large swath of unexplored search space where a successful oscillator discovery could turn out to be any two-digit or low three-digit period.

It's hard to summarize the relative probabilities of finding different periods. For composite periods where a large number of different sparkers are available, of course, it's much easier to complete "partial" patterns. Then, if the new oscillator has any exposed sparks, that means that it might become even easier to complete the next new oscillator at that period.

Similarly, periods with many different factors tend to be easier to complete by applying different sparkers.

For prime periods like 19 and 41 only stable catalysts can be used -- unless an entertaining trick turns up like a blinker catalyst that gets rephased, anyway. Basic statistics tells us that we should expect to find roughly an equal number of oscillators for each two-digit prime period.

-- Roughly. *Very* roughly. In fact, only slightly less basic statistics probably tells us that we shouldn't expect anything like equality among oscillator periods. We're almost guaranteed to end up with "lucky" and "unlucky" periods for as long as the total oscillator count remains small. In practice we'll often find either more or fewer oscillators than we should expect to find, on average, at that period.

Unlucky and Lucky

Obviously 19 and 41 are at the top of our current list of unlucky periods. But the Lucky List is getting very seriously lopsided at this point as well. 23, for example, was still on the Unlucky List less than three years ago. But in the last two days, two different new p23 mechanisms have been discovered, for a total of five: David Hilbert, P23 honey farm hassler, 92P23, P23_pi-heptomino_hassler, and 55P23.

Code: Select all

x = 75, y = 58, rule = B3/S23
61b2o$7b2o15b2o29bob2obobo4bo$8bo15bo30b2obobo4b3o$6bo19bo32b2o3bo$6b
5o11b5o37b2o$10bo11bo30b2o15b2o$4b4o17b4o25bo15bo$4bo2bo17bo2bo25bobo
11bobo$55b2o5b2o4b2o$20b2o40b2o$8b3o3b2ob2o3b4o35bobo$8bo2bo2b2obo5b3o
11bo23b2o$7bo3bo24bobo16b2o4b2o5b2o$7b4o12bo13bo16bobo11bobo$8bo12b2o
31bo15bo$3b2o11b2o4bo2bo2b2o23b2o15b2o$3bo11bo2bo4b2o4bo29b2o$2obo12b
2o11bob2o13bo13bo3b2o$ob2ob2o19b2ob2obo13b3o8b3o4bobob2o$5bo21bo10bo
10bo7bo4bobob2obo$5bobo17bobo9bobo8b2o12b2o$6b2o17b2o9b2ob2o$10bo11bo
14bo2bo$6b5o11b5o5b2o4b2o11bo8bo$6bo19bo4bobo16b3o6bobo$8bo15bo6bo11bo
5bo3bo6bo$7b2o15b2o4b2o9b3o5bob2o$41bo2bo5b2o$40b7o$38b2obo2bobo$39bob
o2bob2o$39b7o$34b2o5bo2bo$33b2obo5b3o9b2o$25bo6bo3bo5bo11bo$24bobo6b3o
16bobo4bo$25bo8bo11b2o4b2o5b3o4b2o$45bo2bo13bo3b2o$45b2ob2o11b2o$36b2o
8bobo$30bo5bo10bo18bo6b2o$18bo9b3o6b3o17b2o6b3o5bo$6bo11b3o6bo11bo17bo
6b4o3bobo$6b3o5b2o5bo5b2o30bo3bo7b2o$9bo4b2o4b2o36b2o2b2o2bo$8b2o47bo
3b3obobo$22b4o22bo7bob2ob3o2bo$18bo3bo2bo21bobo5bo2bobo2bo5bo$9b2o6bo
6bo6b2o15bo6b2o2bo4b5o$9b2o6bo6bo6b2o32b3o$16bo2bo3bo40b3o3b2o$16b4o
43b2o5bobo$32b2o30bo7bo$20b2o4b2o4bo28b3o8b2o$13b2o5bo5b2o5b3o25bo$14b
o6b3o11bo$11b3o9bo$11bo!

The last three were discovered since the beginning of October, and the last two since the beginning of November.

Similarly, 37 is also currently high on the Lucky List, also with five different engines at that period as of this morning. Here's today's p37 oscillator edition (addition?), by Nico Brown.

Code: Select all

#N p37 LOM hassler
#O Nico Brown, 7 November 2022
#C https://conwaylife.com/wiki/Lumps_of_muck_hasslers#p37
x = 44, y = 19, rule = B3/S23
8b2o$7bo2bo$8bobo$9bo26b2o$36bobo$38bo2b2o$12bo24b2obobo$12bo25bobo$2o
9bo18b2o6bob2o$o2bob2o5b2o16b2o5b2obo2bo$2b2obo6b2o18bo9b2o$3bobo25bo$
bobob2o24bo$b2o2bo$5bobo$6b2o26bo$33bobo$33bo2bo$34b2o!

In case it's useful, a list of links for the various prime-period oscillators is currently being kept up to date here.

New Spaceships
Recent discoveries here are difficult to summarize, so I'll just suggest looking through the Spaceship Discussion Thread since the last NewLifeCA message. There are several new spaceships at c/5, for example, plus a number of new greyships, and a few record-breaking small c/2 rakes at various periods.

New Glider Syntheses
If anyone wants to contribute to the project of synthesizing the remaining unsynthesized 21-bit still lifes, now would be a good time. At the rate they're disappearing, there might not be any unsynthesized 21-bit still lifes for very much longer. The current count as of 7 November 2022 is 27 21-bitters remaining, down from well over a hundred a month ago.

RCT Report
The Reverse Caber Tosser project has now produced some very interesting demo patterns. Adam P. Goucher's "semilator" demo design, where everything works exactly the same as in a complete RCT pattern except that some additional data bits are sneaked in in the middle by colliding *WSSes, can build patterns that run very easily in Golly despite their inordinately large size.

The current November 7 demo pattern starts as usual with a nice small population of 80 cells even (plus fifty-six-million-odd more cells consisting of RCT bits stored as *WSSes, but we can ignore those). The glider-producing switch engines increase the population until it passes one quadrillion, topping out at 1,319,193,471,756,825 live cells at the singularity point.

For this demo pattern, the singularity happens around T=2,345,230,320,367 when the pattern reaches the above population. The main GPSE collision completes at T=2,345,230,317,611, but a couple of stray gliders have to be absorbed by a carefully placed ship before the population spikes slightly and then starts dropping again.

These are not really significant numbers, of course. The actual RCT pattern that this demo pattern emulates will have an immeasurably higher maximum population and later singularity point -- but it will still perform all the exact same construction and destruction steps ... eventually.

All that is left now is to add a recipe to clean up the relatively small circuitry of the DBCA, the Decoder and Better Construction Arm -- and to finally get around to actually building the ATBC, the Actual Thing Being Constructed, which is the real purpose of this entire unreasonable exercise. We have ATBC seeds all ready to go, so the DBCA destruction is really the only unfinished piece.

It's usually not such a good idea to make predictions about these kinds of mega-projects, but it currently doesn't look as if that unfinished piece will remain unfinished for much longer.

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #28, 11/9/2022 2:07pm

NewLifeCA #28, 9 November 2022: new p25 gun, GGG from soup, RCT with labels

It seems like the most interesting things usually happen just a day or two after one of these news items goes out, such that a follow-up is needed. Here are some of the new developments since two days ago:

1) A new true period 25 glider gun has been found. A glider will leave the bounding box on the next tick, even though there's no glider there at T=0 -- so I believe this is the correct bounding box to measure for calculating the "official" size of the gun:

Code: Select all

#N p25 glider gun
#O Mitchell Riley, 7 November 2022
#C Bounding box reduced by iNoMed
#C https://conwaylife.com/forums/viewtopic.php?p=153250#p153250
x = 23, y = 22, rule = B3/S23
11b2o4b2o$11bobo2bobo$13bo2bo$12b2o2b2o$11b3o2b3o$13bo2bo$6b2o$7bo6bo$
7bobo$5b2ob2o2b3o$4bobo5b2obo$4bobo8b3o2bobo$2b2obob2o3b2o3b2o3bo$3bob
o3bo5bo6bo$3bobob2o7bo4bo$2obobobo10b2o$o2b2obo$2bo4bo$3b5o2$2bob2o$2b
2obo!

Anyone care to give an opinion on whether this would "traditionally" have counted as a 23x22 gun in Jason Summers' or Chris Cain's collections? Or does there have to be an existing glider in the bounding box, for it to be able to leave the bounding box on the next tick? In that case we'd have to bump the bounding box up to 24x22. We don't see this situation very often, it seems.

2) A symmetric soup has finally turned up on Catagolue that produces a Gosper glider gun variant:

Code: Select all

#C https://catagolue.hatsya.com/object/yl30_1_20_ecdb123bc1508794fb30325babb8ba21/b3s23
#C https://catagolue.hatsya.com/hashsoup/C4_4/o_hjWdgGhm7agu146534448/b3s23
x = 32, y = 32, rule = B3/S23
o2b2o2bo2bobo2bo2bob2ob2obo3b2o$2obobo2b3ob2obob3o3b4o3bo$5b2o2bobo2b
2obo5b5o$3b6ob4ob2obob3ob2ob2ob2o$2b2o3b2ob4obobob2obobobobo2bo$3ob3ob
7obo4bob4ob3o$b3obobo2bobob3o5b3obob2o$8obobo3bo2b2obob3ob2o2bo$3o2b4o
3b3o3bob2obo2b3obo$3b2obo3b4ob2o3bo3bobo2b2o$o2bobob2o2bo2b5obobo2b4ob
2o$o2b2o3b6o4b5obob4o$bo2bo2bo3bo2bob3obob2ob4ob2o$2obo3b2ob3o2bobo2bo
b2o2b3obo$b2obo5bob4obobobobob2o2bo$3bob2o2b2obo4b2o2b2ob2ob5o$5ob2ob
2o2b2o4bob2o2b2obo$2bo2b2obobobobob4obo5bob2o$bob3o2b2obo2bobo2b3ob2o
3bob2o$2ob4ob2obob3obo2bo3bo2bo2bo$2b4obob5o4b6o3b2o2bo$2ob4o2bobob5o
2bo2b2obobo2bo$b2o2bobo3bo3b2ob4o3bob2o$bob3o2bob2obo3b3o3b4o2b3o$o2b
2ob3obob2o2bo3bobob8o$2b2obob3o5b3obobo2bobob3o$b3ob4obo4bob7ob3ob3o$o
2bobobobob2obobob4ob2o3b2o$2ob2ob2ob3obob2ob4ob6o$4b5o5bob2o2bobo2b2o$
bo3b4o3b3obob2ob3o2bobob2o$2o3bob2ob2obo2bo2bobo2bo2b2o2bo!

Of course the symmetry is mostly incidental to the formation of the (asymmetrical) gun engine; it just allows the queen-bee shuttles' beehives to mutually annihilate, such that the whole thing survives to be catalogued by apgsearch. The two queen bees are definitely implicit in each quarter-soup at T=0:

Code: Select all

x = 37, y = 21, rule = LifeHistory
35.2C$35.C$33.C.C$33.2C3$2C3.C2.2A2.A2.A.A2.A2.A.2A.2A.A3.2E$2C3.2C.A
.A2.3A.2A.A.3A3.4A3.E$10.2A2.A.A2.2A.A5.5A$8.C5A.4A.2A.A.3A.2A.2E$8.D
3.2A.4A.A.A.2A.A.A.E$9.DCA.7A.A4.A.2A2E$10.C.A2.A.A.3A5.2AE$11.2C.A.A
3.A2.2A.A.2E$12.2C3.3A3.A.2A.E$15.4A.2A3.A$16.A2.5A.A$16.C2A4.A2E$16.
C2.A.2AE$17.C2.A.E$18.2CA.E!

3) Progress continues on the RCT project. Here is an "RCT viewer" script, which is now generated as part of the build process for each pattern.

The script runs the latest RCT pattern and does a lot of the zooming and speed changes for you, while describing what's going on in each stage in Golly's status bar.

The current RCT manages to build an entire Decoder and Better Construction Arm plus a west-traveling MWSS and a stray block or so, with only sixteen gliders. After the next rebuild or three, it will start building a Hensel decimal counter instead (and no MWSS) with basically the same sixteen gliders, spaced even more monstrously far apart than they are already.

(Again, we're ignoring the *WSSes to the west and south, which can be thought of as just a sneaky way to emulate the full pattern pretty much perfectly using standard HashLife, without making Golly deal withthe ridiculously large numbers that would show up in the non-emulated 16-glider pattern.)

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #29, 11/10/2022 8:52am

NewLifeCA #29, 10 November 2022: the RCT project is complete!

Here's a rare single-topic NewLifeCA news flash: in message #27 I wrote

It's usually not such a good idea to make predictions about these kinds of mega-projects, but it currently doesn't look as if that unfinished piece will remain unfinished for much longer.

Yesterday evening, Pavel Grankovskiy completed the final subtask needed to construct a complete demo pattern for a 16-glider RCT-based construction of Alan Hensel's 1994 decimal counter.

The same post also contains an updated viewer script, showing how the various stages of construction and destruction work in detail.

As usual, extra *WSSes are included to emulate a full RCT pattern while keeping the pattern size down to something that Golly can easily run. However, Grankovskiy did also successfully compile a true 16-glider RCT encoding of a Hensel decimal counter, in macrocell format.

It turned out to be possible to open the resulting 140MB file in Golly, but it appeared to be beyond Golly's current design capacities to run the pattern long enough to see any amount of construction happening. Discussion on this topic happened in the ConwayLife Lounge on Discord.

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #30, 11/18/2022 12:33am

NewLifeCA #30, 18 November 2022: RCT15, a true p34 gun, and a flood of oscillators

The Magic Number Is Now 15

After a few days of highly non-trivial adjustments to the RCT16 design, Pavel Grankovskiy has completed a slightly larger pattern that completes the same construction of a Hensel decimal counter, starting with only 15 gliders instead of 16.

"Slightly larger" means that the diameter of the RCT15 pattern is, roughly speaking, a mere 2^15000 times bigger than the RCT16 pattern. That may seem like a big number, but on the scale of these constructions it's barely noticeable. The extra cost is due to the initial elbow being generated very close to the epicentre collision point, so that it has to be pushed some distance away before the construction of the DBCA can begin.

The 2^15000 number is very approximate, because minor optimizations to the recipe are still going on. It's technically possible, though by no means simple, to optimize the new RCT15 to reach a smaller size than the current RCT16. On the other hand, if similar optimizations were applied to the RCT16 design, then that pattern would become smaller than the RCT15 again. Now that RCT15 is available, though, it's unlikely that any more time will be spent improving RCT16.

Two blog posts have been completed, to explain different aspects of the RCT's convoluted internal workings and equally convoluted history. I posted a summary article here, and Brett Berger went into more detail in another blog post here.

A True-Period P34 Gun
-------------------------------
November 17th was a big day for new discoveries in the oscillator and gun departments. The biggest find was the first-ever true period 34 gun, shown here with a known period-tripling p34-specific eater:

Code: Select all

#N True-period P34 gun
#O Nico Brown, 17 November 2022
#C https://conwaylife.com/forums/viewtopic.php?p=153747#p153747
#C https://catagolue.hatsya.com/object/guntrue_34/b3s23
#C EDIT 11/19/2022 reduced catalysts using beehive stabilization
x = 62, y = 47, rule = B3/S23
28b2o6bo$29bo6b3o$29bobo7bo$30b2o6bo$4b2o32bo2bo$5bo2b2o31bo$5bobobo3b
o12b2o13bo$6bo6b3o11bo$16bo10bobo11bo$2b2o11b2o11b2o4b2o3bobo$bo2bo28b
o2bo3b2o$bob2o5b3o20bobo$2o8bo22b3o13b3o7b2o$o2b2o6bo14b2o21bobo6bo2bo
$b2o2bo19bo2bo14b2o3bo2bo4bo2b2o$3b2obo2b2o4b3o6b2obo15bobo3b2o4bob2o$
b2o2bo3b2o6bo7b2o16bo12bo2b2o$o2bo11bobo39b2o2bo$b2o13bo5bo20bo6bo9b2o
$21bobo19bo5bobo5b2obo$12b2o7bo21bo2bo10bo2bo$11bob2o6b3o8b2o12bo11b2o
$10bo2bo18bobo10bo$11b2o14bo6bo11b3o6bo$28bo5b2o12bo3bobobo$26b3o23b2o
2bo$56b2o$22b2o$22bo$23b3o$25bo12$36b3o3b3o2$40bo$40bo$40bo!

The same post also contains a new true-period p74 gun -- but we already had one of those, since that's the lowest speed at which a syringe can be overclocked.

A Great Day for Honeyfarm Hasslers
-------------------------------------------------
The new catalyst that appears in both the p34 gun and the p74 gun seems to be an unusually prolific source of new honeyfarm-hassling engines. In just one post, Nico Brown presented five more new oscillators using this same catalyst, with periods 43, 52, 59, 83, and 102.

More New Catalysts
Other interesting reactions are turning up surprisingly often, involving complex still lifes that (I think, for the most part) were never known to have any catalytic effects before. It's a bit beyond the scope of a NewLifeCA post to summarize them all, but besides the catalyst in the above guns and oscillators, here is a sample of catalytic reactions posted to the forums in the last twenty-four hours.

The linked post is by Carson Cheng, with more reactions added by Mitchell Riley in the next message. These catalysts, and others like them, might well produce more new oscillator results once they've been run through the new crop of search utilities.

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #31, 12/1/2022 9:12pm

NewLifeCA #31, 1 December 2022: methuselah record, brain synth, and unidimensional spaceship plans

December already! I'd better get caught up on current events before the Christmas rush starts. (People tend to find more time for Life projects over the holidays, so things can get busy around the New Year.)

Monster Methuselahs
First, y'all may or may not remember the "really big record-breaker" 16x16 methuselah by dani, from NewLifeCA #22, which stabilizes in 4,764,364 ticks. A few months later, on October 20, a new forum member with the handle "gravity" came up with a 20x20 methuselah with a lifespan of 13,629,876 ticks.

For some reason it looks like I missed mentioning all of this in NewLifeCA messages... but dani adjusted the original methuselah to get a reduced-population equivalent, with 27 cells --

Code: Select all

x = 22, y = 20, rule = B3/S23
5b4o$9bo$9bo$10b2o6$o$o$o$b2o$b3o$b2o$19bo$18bo$17bo2bo$18bo2bo$19b3o!

-- and Tanner Jacobi produced a reduced-bounding-box version.

Code: Select all

x = 20, y = 16, rule = B3/S23
5b4o$9bo$9bo$10b2o4$15bo$16bo$o13b2o$o15bobo$o15bo$b2o11bo$b3o11b3o$b
2o12bob2o$18b2o!

It's a bit difficult to know exactly what to optimize first with these things. Obviously the lifespan could be increased also, probably at the cost of increasing either bounding box or population -- or both, but that definitely wouldn't be interesting: if there's one thing these methuselahs don't seem to need, it's another extra few ticks before stabilization.

On November 21, "gravity" showed up again with another 20x20 methuselah. This one lasts almost an order of magnitude longer -- 126,932,978 ticks (!). It was also reduced to 27 cells, this time by toroidalet.

Code: Select all

x = 23, y = 21, rule = B3/S23
6bobo2$5bobob2o$11bo2$11b2o5$bo$obo$19bobo$o2bo18bo$2b2o14bo2bo$3bo14b
2o3$16bo$16bo$16bo!

Several other possible variations showed up, but none of them seem particularly worth quoting here in pattern form.

Brain Surgery
People have been trying to figure out how to construct a "brain" spaceship since at least 2015. Goldtiger997 completed a recipe a few days ago:

Code: Select all

#N brain spaceship continuous synthesis
#O Goldtiger997, 25 November 2022
#C https://conwaylife.com/forums/viewtopic.php?p=154110#p154110
x = 295, y = 271, rule = B3/S23
26bo241bo$27bo239bo$25b3o239b3o5$30bo233bo$31bo231bo$29b3o231b3o2$46bo
bo$41bo5b2o$39bobo5bo$22bo8bo8b2o221bo8bo$23bo8bo229bo8bo$21b3o6b3o
229b3o6b3o$18bo257bo$16bobo257bobo$17b2o257b2o3$22bo249bo$23bo247bo$
21b3o247b3o17$26bo241bo$24bobo241bobo$20bo4b2o241b2o4bo$21b2o249b2o$
20b2o251b2o7$41bo$42bo$40b3o3$53bo11bo163bo11bo6bo$51bobo12b2o159b2o
12bobo3bo$52b2o11b2o161b2o11b2o4b3o13$77bo139bo$78b2o135b2o$77b2o137b
2o5$70bo153bo$71b2o149b2o$70b2o5bo139bo5b2o$75bobo139bobo$76b2o139b2o
3$207bo$205b2o$206b2o3$92bo$93b2o94bo$92b2o93b2o$188b2o$119bo$120b2o$
110bo8b2o80bo$111b2o87bo$110b2o88b3o$170bo$168b2o$98bo70b2o$99bo90bo$
97b3o89bo$125bo63b3o3bobo$123bobo69b2o$124b2o70bo$109bo61bo$110bo58b2o
11bo$102bobo3b3o59b2o10bobo$103b2o77b2o$103bo2$117bo$115bobo$116b2o41$
111b2o$112b2o$93b3o15bo9b2o49b2o$95bo24bobo49bobo$94bo27bo49bo$187b2o$
186b2o$97b2o89bo15b3o$96bobo105bo$98bo17b3o86bo$118bo$117bo$201b2o$
201bobo$181b3o17bo$181bo$182bo3$181bo$104b2o74b2o$105b2o73bobo$104bo$
175b2o7bo$175bobo5b2o$175bo7bobo3$105b2o$104bobo$106bo6$78b2o135b2o$
79b2o133b2o$78bo15b2o112bo7bo$95b2o110b2o$94bo112bobo2$63bo27b2o6b3o
129bo$63b2o27b2o7bo128b2o$62bobo26bo8bo129bobo3$206b3o$206bo$207bo3$
71b2o$70bobo$72bo$75b2o$76b2o$75bo139b2o10b2o$215bobo9bobo$215bo11bo$
223b2o$222b2o$73b2o149bo$36bo35bobo$36b2o36bo$35bobo2$68b2o$69b2o155b
3o$68bo157bo5bo$227bo3b2o$231bobo8$55b3o179b3o$57bo179bo$50bo5bo181bo
5bo$50b2o191b2o$15b3o31bobo191bobo31b3o$17bo259bo$16bo261bo3$57bo$57b
2o$56bobo3$28b3o211bo21b3o$30bo210b2o21bo$3o26bo211bobo21bo26b3o$2bo
289bo$bo291bo8$24b2o243b2o$25b2o11b2o228b2o$24bo7b2o3bobo221b2o7bo$33b
2o4bo220b2o$32bo218b3o8bo$251bo$14b2o236bo$13bobo$15bo!

Can't Get Any Thinner
Last but not least, momentum has been growing recently on the unidimensional spaceship project. This is a hypothetical one-cell thick pattern that travels across the Life plane at some as yet unknown painfully slow speed and high period. The newest design borrows some mechanisms from the recently completed RCT15 project, but it won't have to be nearly as large or as difficult to simulate as an RCT pattern. The relevant thread starts here, and the most recent burst of activity began on November 25.

Looks like this might be an interesting project to keep an eye on!

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #32, 12/4/2022 12:19am

NewLifeCA #32, 4 December 2022: new strictly volatile oscillators

On December 2, Nico Brown published a Golly script that can build a strict volatility-1 oscillator with any period 949 or greater.

3,506,910 was the previous minimum period above which there was a known way to create a strict-volatility-1 oscillator of any period.  Moving that minimum value all the way down to 949 was quite a large and sudden improvement!

The resulting oscillators are enormous, to the point that it's somewhat difficult for Golly to work with them.  With a population over 594 million in a bounding box 1.4 million cells on a side, these might be considered to be the new "largest interesting patterns" that have been constructed so far.  Even an 0E0P metacell has a population of only around 18 million.

Caterloopillar Comparison
Each oscillator can be described as a set of four bi-directional shotguns arranged in a huge square.  Each of the four shotguns constructs two fleets of *WSSes heading in opposite directions.  Each of these fleets interacts with an arrangement of blocks to create diagonal salvos of gliders that construct the *WSS fleet that travels the other way.

In a conventional Caterloopillar, loaves are used instead of blocks to store construction information.  The presence of a loaf in the path of a Caterloopillar *WSS convoy triggers the creation of a glider.  The loaves move forward or backward as each convoy passes, keeping up with the Caterloopillar's overall movement.

In the new oscillators, very similarly, a glider is emitted each time a convoy of *WSSes passes a block.  The block is temporarily displaced but ultimately returns to the exact same location.

Caterloopillar Contrast
The fact that the blocks don't move makes it a much bigger task to create slow salvos that build opposing *WSS fleets.  In a conventional Caterloopillar, one small *WSS convoy can progressively construct different stages of a slow-salvo recipe as it moves along a single line of loaves.

In the new oscillators, the next *WSS convoy to reach a given block will generate the next glider in the same exact place as the last one.  That means it's necessary to stack up multiple units of these glider-emitting *WSS convoys next to each other to create workable *WSS-building salvos of gliders.

Unlike conventional Caterloopillar recipes, these glider salvos are *not* slow salvos necessarily.  They're just constructible groups of gliders that hit target blocks and produce edgy *WSSes traveling in the correct direction ... plus, eventually, new target blocks in the exact same locations.

In all, over 200 convoys of block-reading *WSSes make up the complete fleets traveling in each direction  -- 211 convoys each way, if I've counted right.  Maybe a good way to think of the huge bi-directional *WSS-fleet shotgun would be "211 concentric speed-0 Caterloopillars".

Stopping the Convoys
Instead of suppressing the *WSS fleets at both ends with specially designed absorber mechanisms, as conventional Caterloopillars do, these oscillators use identical mirrored copies of the base *WSS-fleet shotgun, arranged in the square pattern mentioned above.  Each block-reading convoy contains extra *WSSes as needed to ensure clean mutual annihilation with an identical convoy coming in at 90 degrees.

There are quite a few additional subtleties hiding in the oscillator builder script.  For example, there are two distinct *WSS convoys for each direction of travel, corresponding to the parity of the glider being generated.  Convoys crash into each other differently at the corners depending on their parity, so different *WSSes have to be added in each case to make sure that the corner crashes are completely clean.

-- That's about as much as I think I understand at the moment.  As it is, if someone points out mistakes in my summary, I may have to send along a correction or two.
 
Keep the cheer,


Dave

[dvgrn]

NewLifeCA #33, 1/13/2023 4:52m

NewLifeCA #33, 13 January 2023: Wonderful Walrus, POTY Prep, Minimizing Max, Constructible C/3s, Lisp in Life

What?! Wow!
The Life universe's first c/8 diagonal spaceship has showed up in an ikpx2 search, and it's surprisingly small:

Code: Select all

#N walrus
#O Adam P. Goucher, 12 January 2023
#C https://conwaylife.com/wiki/Walrus
x = 20, y = 19, rule = B3/S23
5b4o$5bo2bo$4bo5bo$3bo5b2o$o4b4obo$o4bob4o$o3bo3b3obo$2bobo2bo7b2o$15b
3o$2o3b2o8bo2b2o$2ob2ob3o2bo2bo$b2o10bo$3bo$3bo5bo$8b2o$8bo2$8b3o$8b3o!

Another spaceship discovery since the last NewLifeCA message was Frank Everdij's spaceship from back on December 5, the third elementary c/7 orthogonal ship known. It is also relatively small and also found with ikpx2, but completed manually by connecting two mirrored copies of a partial that starts from a loafer front end:

Code: Select all

#N taco
#O Frank Everdij, 5 December 2022
#C https://conwaylife.com/wiki/Taco
x = 29, y = 25, rule = B3/S23
bo25bo$obo23bobo$o2bo21bo2bo$b2o23b2o2$o27bo$bo25bo$2o25b2o$o4bo17bo4b
o$4bobo15bobo$3bo21bo$4b2o17b2o$3bo21bo$4b3o15b3o2$4b2obo13bob2o$4bobo
bo11bobobo$6bo2b2o7b2o2bo$5bobo13bobo$7bo13bo$5b2o15b2o$9b2o7b2o$9b2ob
o3bob2o$10bo7bo$11b3ob3o!

Prolific POTY Participation
2022 was another good year for new Life discoveries, with a record number of news items added to LifeWiki -- 136 CurrentNews items, compared with 72 from 2021 and 47 in 2019.

Some of this was due to ongoing attempts to finish off the last few unknown periods and prove that Life is in fact omniperiodic. Periods 19 and 41 haven't showed up yet, but lots of new oscillators of other periods have appeared that improved on various existing records.

Another reason for the high count is that CurrentNews just plain has more editors than it did a few years ago, so we aren't missing as many new developments. Still, 2022 was definitely a good year.

-- Speaking of which, new oscillator discoveries are still trickling in, like this interesting set variants of a new p18 mechanism from Catagolue today (brought to you via Discord discussion):

Code: Select all

#C p18 oscillator variants, plus a way to trigger the base reaction at p30
#C https://discord.com/channels/357922255553953794/370571014654001154/1063554766573162496
x = 68, y = 50, rule = B3/S23
47bo$47bo4b2o$4bo38bo3bo4bo2bo$4bo4b2o30b2o11bo4b2o$4bo4bo2bo30b2o8bo
3bo2bo$11bo4b2o24bo3b3o8b2o$3o7bo3bo2bo35bobobo$14b2o29bo3bo3b2obo2bo$
10bobobo31bobo7bob2o$9bob2obobo30bo8bo$9bo5b2o25b2o2b3o2b2o2b2o$b2o4b
3o32bo9bo$bo2bobo36b2o5b2o$3bo3bo$2bo3b2o35b2o5b2o$42bo9bo$4b4o34b2o2b
3o2b2o$5bo2bo38bo$3bo3b2o37bobo$3b2o40bo3bo2$46b3o4$8b2o$9bo5b2o$9bob
2obobo$10bobobo19b2o$14b2o18bo2bo$10bo3bo2bo8b5o7bo7bo$11bo4b2o7bo5bo
6bo6bo$4bo4bo2bo12bo3b2o7bo5bo2bo$4bo4b2o15bo7bo2bo8b2o8b2o3b2o$4bo29b
2o20bobobobo$58bobo$3o50bo11bo$51bo2bobo5bobo2bo$46b3o2bo3b2o5b2o3bo$
51bo2bobo5bobo2bo$9bo43bo11bo$b2o4b3o40bo7bobo$bo2bobo41bobo5bobobobo$
3bo3bo41bobo4b2o3b2o$2bo3b2o41bo2$4b4o$5bo2bo$3bo3b2o$3b2o!

Max Much More Minimized
The Max article on LifeWiki has the details.

Code: Select all

#N 107-cell 25x23 Max variant
#O Rocknlol, 8 January 2023
#C https://conwaylife.com/forums/viewtopic.php?p=155703#p155703
x = 25, y = 23, rule = B3/S23
19b3o$13bo5bo2bo$13bo5bo$11bo2bo4bo$11b4o4bo$3bo7b2o3bo2bo$o9bo9bo$b2o
5bo3bo10bo$4bo3bo3bo9bo$2obob2obo3bo3b2o4bo$4bo5bo3b2o4bo3bo$2bob2o2bo
3bo3bo2b2obo$o3bo4b2o3bo5bo$2bo4b2o3bo3bob2obob2o$2bo9bo3bo3bo$bo10bo
3bo5b2o$4bo9bo9bo$5bo2bo3b2o7bo$5bo4b4o$5bo4bo2bo$5bo5bo$2bo2bo5bo$3b
3o!

Code: Select all

#N 142-cell 21x19 Max variant
#O Rocknlol, 8 January 2023
#C https://conwaylife.com/forums/viewtopic.php?p=155703#p155703
x = 21, y = 19, rule = B3/S23
8bo2b3o3b3o$bo5bo3b2o4bo2bo$ob3ob3o8bo$2bo2b2o3b3o3bobo$o4bo3b2obob2o
2bo$2obo2bo7b2ob3o$2bo4bo3b4obo2bo$11bobo$3b4o2bo2bobo2b2obo$4o4bo3bo
4b4o$ob2o2bobo2bo2b4o$7bobo$bo2bob4o3bo4bo$b3ob2o7bo2bob2o$2bo2b2obob
2o3bo4bo$2bobo3b3o3b2o2bo$3bo8b3ob3obo$o2bo4b2o3bo5bo$b3o3b3o2bo!

Cutting Constraints on Constructing C/3 Chains
One of the surprises from the end of 2022 was a the discovery of glider construction recipes for an infinite family of c/3 spaceships -- or several infinite families, depending on how you count these things, but the extensible wave in the middle is common to all families. (NB: Click on the individual spaceships in the list in the link, and scroll down to see their glider construction recipes.)

Spaceship Syntheses and Such
Goldtiger997 has figured out two more final activation steps for previously unsynthesizable spaceships:

Code: Select all

#C https://catagolue.hatsya.com/object/xq5_f930sgy1gs039fz24dcpn03330npcd42zy13iv0vi3/b3s23
#C https://catagolue.hatsya.com/object/xq4_y258880638gszwu1w32gkoz34j0ozx11/b3s23
x = 119, y = 57, rule = B3/S23
65bo$66b2o42bobo$65b2o15bo27b2o$29bobo48bobo16bo11bo$29b2o50b2o15bo$
30bo8bo30bo27b3o$11bo25b2o24bo4bobo$9bobo26b2o24b2o3b2o$10b2o51b2o41bo
6bobo$104b2o7b2o$61bo43b2o7bo$59bobo$22bobo7bo27b2o5bo$5bobo14b2o8bobo
33bo$6b2o4bo10bo8b2o32b3o$6bo3bobo67b2o4b2o$11b2o67bo4bo2bo$2bo68bo9bo
3bo2bo7b3o$obo20bo32bo15b2o8bo3b2o$b2o19bobo29bobo14b2o10bo$21bob2o30b
2o27bo5bo$21bo41bo21bo5b2o$20b2o14bo24bobo16b2o2b2o3b2o$13b2o20b2o25b
2o16b2o2bo6bo$11b3obob2o16bobo47bo8bo$10bo4bobo66b2o7bobo$10b6o2b3o62b
o9bobo$16b2o3bo61bob3o6bo8b2o$10b6o2b3o63bobobo14bobo$10bo4bobo70bo14b
o$11b3obob2o61bo7b2o25bo2bo$13b2o63bobo33bo$20b2o7bo49bobo32bo3bo$21bo
7bobo47bo34b4o$21bob2o4b2o52b2o5bo$b2o19bobo57bo2bo3bobo$obo20bo37b2o
20b2o4bobo$2bo28b3o26bobo12bo14bo$11b2o18bo30bo12bo$6bo3bobo19bo42bo
28bo$6b2o4bo10bo79b2o$5bobo14b2o79bobo5b2o$22bobo31b2o52b2o$55bobo54bo
$57bo28b2o$86bobo18bo7b3o$10b2o54b2o18bo19b2o7bo$9bobo55b2o37bobo7bo$
11bo54bo22b3o$30bo44b2o12bo$29b2o43bobo13bo19b3o$29bobo27bo16bo33bo$
59b2o19b3o28bo$58bobo21bo$66bo14bo$66b2o$65bobo!

This brought up the total to ten newly synthesizable spaceships in 2022: Orion 2, 33P4H1V1, 70P5H2V0, 58P8H4V0, 30P3H1V0, 29P3H1V0,
brain, and the above 66P5H2V0 and 37P4H1V1 -- plus the infinite family of c/3 spaceships mentioned above.

Lisp in Life
This is actually very old news, from a blog post from 12 January 2022, but it had not gotten much attention on the forums until its POTY nomination. Hikaru Ikuta completed a Lisp interpreter using technology similar to the Quest for Tetris project from several years ago. As far as I know this is the first implementation of a
standardized high-level programming language inside Conway’s Game of Life.

----------------------------

It will be interesting to see what shows up in the rest of 2023!

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #34, 1/15/2023 10:40am

NewLifeCA #34, 15 January 2023: more about Pattern of the Year, among other things

No huge new discoveries have showed up since the last NewLifeCA message, and there haven't been any reports of details that desperately need correcting.

After a second reading, though, I'm remembering that I meant to say more about the Pattern of the Year 2022 competition -- or maybe "event" is a better word for this annual conwaylife.com tradition:

viewtopic.php?f=2&t=5910
https://conwaylife.com/wiki/User:Macbi/ ... ominations

As of today, all but half a dozen or so of the links and descriptions have been filled out, so POTY 2022 might be ready for voting relatively soon.

If you remember something POTY-worthy that hasn't been nominated yet, want to help with the remaining descriptions, or if you might have missed some of the excitement in the last year, now might be a good time for a quick review. I'll send another update when it's actually time for the voting to start.

Minor Miscellany
----------------------
While I'm emailing again, here are a few recent items that didn't rise to the level of Current News, but might still be interesting to the NewLifeCA group.

A fourth symmetric soup containing Gosper glider guns turned up in Catagolue recently, courtesy of Open Science Grid:

https://catagolue.hatsya.com/census/b3s23/C4_4/yl30

Charity Engine recently sent to Catagolue a new eater for Jason's p156 glider pairs, the northwest corner one here (the other symmetric eaters have showed up many times by now):

Code: Select all

x = 62, y = 60, rule = B3/S23
3b2o$3b2o$59bo$2o56bobo$2o9bo46bo2bo$10bobo46b2o$10bobo$11bo3$5b2o$4bo
2bo23b2o$5b2o24b2o5$33b2o$32b2o$33b2o10$44bobo$44b3o$11b2o32bo5b2o$11b
2o5bo32b2o$17b3o$17bobo10$29b2o$30b2o$29b2o5$31b2o$31b2o4$2bo54b2o$bob
o52bo2bo$bobo52bo2bo$2bo54b2o!

Linear-growth patterns based on Jason's p156 have showed up in thousands of symmetric soups by this time --

https://catagolue.hatsya.com/census/b3s23/D4_x4/yl312

-- and oscillators do show up occasionally, but not incorporating the new eater yet:

https://catagolue.hatsya.com/census/b3s23/D4_x4/xp312

There hasn't been an "xp156" oscillator yet. It would take considerably more luck to drop fishhook eaters or these new beehives-and-blocks eaters on both [sets of] output lanes, to avoid the period-doubling effect of the other likely known glider-absorbing mechanisms.
.
Here's one use that has been found for the unusual sparks in the new p18 oscillator from the last message:

Code: Select all

#C p36 honeyfarm hassler
#C reduced by 83bismuth38 and JP21, 14 January 2023
#C https://conwaylife.com/forums/viewtopic.php?p=155989#p155989
x = 51, y = 38, rule = B3/S23
23b2o$23bo$18b2obobo$18bob2ob2o$22bo3b3o$13b2o4b2o2b2o2bo$14bo3bo2bob
2o$9b2obo5b2o3bo$9bob3o17b2o$31bo$10b2o17bobo$10bo12b2o4b2o$11bo3bo6bo
2bo$8b3o3bob2o5b3o$2b2o4bo6b2o7bo$2bo2b2obo28bo4bo$3bobobo29bo3b2o$2b
2o33bo3bobo$o2bo11b3o24bo6b2o$2o6bo24b3o11bo2bo$7bobo3bo33b2o$8b2o3bo
29bobobo$8bo4bo28bob2o2bo$26bo7b2o6bo4b2o$25b3o5b2obo3b3o$25bo2bo6bo3b
o$20b2o4b2o12bo$19bobo17b2o$19bo$18b2o17b3obo$27bo3b2o5bob2o$26b2obo2b
o3bo$23bo2b2o2b2o4b2o$22b3o3bo$26b2ob2obo$27bobob2o$27bo$26b2o!

Goldtiger997 pointed out a workable mechanism for a stable Heisenburp for the new c/8 walrus spaceships, though the current proof-of-concept is badly in need of optimization:

viewtopic.php?p=155907#p155907

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #35, 2/28/2023 5:01pm

NewLifeCA #35, 28 February 2023: synthesizable spacefiller, c/3 pseudo-Heisenburp, and a new minstrel


Spacefiller Seed!
I'll mention the freshest news first: Goldtiger997 has found a way to turn a large bait object into a spacefiller by hitting it with (an impressively large number of) gliders.

It looks like spacefillers will soon be joining the ranks of the glider-constructible, and therefore among other things they will be buildable with a universal construction arm, and there will be a 15-glider RCT recipe for them.

None of this is quite true *yet*, though. It's easy (though tedious) to build and synchronize one-glider seeds for the four trigger glider salvos, but there's still some research to do on how to build the impressively large initial still life. Recipes for the surrounding objects have all been figured out at this point.

Here's a comparison of the activation steps for the spacefiller at right (where we don't yet know exactly how to construct the bait constellation) and a medium-sized Canada Grey greyship at left (where we do know how to construct the bait constellation). You can see the similarities at the north ends of the two target objects.

Code: Select all

x = 318, y = 153, rule = B3/S23
191bo89bo$192b2o85b2o$102bo88b2o17bo69b2o$38bobo61bobo7bobo83bobo7bobo
61bobo$39b2o61b2o8b2o85b2o8b2o61b2o$39bo8bobo62bo85bo62bobo8bo$49b2o
211b2o$34bo14bo68bo75bo68bo14bo$32bobo83bobo61bobo7bobo83bobo7bobo$33b
2o7bo56bo4bo5bo7b2o63b2o8b2o7bo5bo4bo56bo7b2o8b2o$40bobo56bobo2bobo3bo
bo70bo16bobo3bobo2bobo56bobo16bo$41b2o56b2o3b2o4b2o89b2o4b2o3b2o56b2o$
34bobo79bobo75bobo79bobo$35b2o79b2o69bo7b2o79b2o7bo$35bo81bo70b2o5bo
81bo5b2o$41bo69bo71bo3b2o12bo69bo12b2o3bo$42bo67bo70bobo18bo67bo18bobo
$40b3o67b3o69b2o16b3o67b3o16b2o$171bo129bo$23bo105bo39bobo129bobo$21bo
bo105bobo38b2o129b2o$22b2o8bo87bo8b2o61bo87bo$33bo85bo62bobo8bo85bo8bo
bo$25bobo3b3o85b3o3bobo55b2o6b3o85b3o6b2o$26b2o97b2o56bo105bo$26bo99bo
3$179bo113bo$24bo103bo51bo3bobo99bobo3bo$25b2o99b2o50b3o4b2o99b2o4b3o$
24b2o101b2o41bo14bo101bo$168bobo$169b2o$20bo111bo43bobo115bobo$21b2o
107b2o41bo3b2o115b2o$20b2o109b2o38bobo3bo117bo4bo$69bo13bo88b2o55bo13b
o55bo$68bobo11bobo82bobo58bobo11bobo54b3o$69bo13bo84b2o59bo13bo61bo$
58b2o10b3ob2ob2ob3o10b2o73bo49b2o10b3ob2ob2ob3o10b2o49bo10bo$58bobo11b
obo3bobo11bobo123bobo11bobo3bobo11bobo49b3o3bo3bo$59b2o14bobo14b2o125b
2o14bobo14b2o55bo4b3o$73b3ob3o153b3ob3o69b3o$72bo7bo151bo7bo$8bo53bo8b
obo5bobo8bo53bo77bo8bobo5bobo8bo$9b2o50bobo8b2o5b2o8bobo50b2o65b2o10bo
bo8b2o5b2o8bobo10b2o$8b2o52b2o2b2o8bo8b2o2b2o52b2o63bobo11b2o2b2o8bo8b
2o2b2o11bobo$13bo52bobo3b9o3bobo52bo69bo16bobo3b9o3bobo16bo$14b2o51bob
obo9bobobo51b2o88bobobo9bobobo$13b2o46b2o6bob11obo6b2o46b2o73bo7b2o6bo
b11obo6b2o7bo$54b2o5bobo5bo13bo5bobo5b2o113bobo6bobo5bo13bo5bobo6bobo$
53bo2bo5bobo5b13o5bobo5bo2bo113bobo6bobo5b13o5bobo6bobo$53bobo7bobobo
17bobobo7bobo114b2o7bobobo17bobobo7b2o$54bo3b2o5bob19obo5b2o3bo62bo2bo
bo51b2o5bob19obo5b2o$57bo2bo4bo21bo4bo2bo63bobo3b2o38bo11bo2bo4bo21bo
4bo2bo11bo47bobo$57bobo6b21o6bobo64b2o3bo39bo11bobo6b21o6bobo11bo47b2o
$58bo3b2o25b2o3bo110bo12bo3b2o25b2o3bo12bo48bo$54b2o5bob27obo5b2o115b
2o5bob27obo5b2o$53bo2bo4bo29bo4bo2bo113bo2bo4bo29bo4bo2bo$53bobo6b29o
6bobo63bo42b2o5bobo6b29o6bobo5b2o$54bo3b2o33b2o3bo65bo40bobo6bo3b2o33b
2o3bo6bobo$57bob35obo66b3o39bobo3b2o5bob35obo5b2o3bobo$57bo18bo18bo
107bobo3bo2bo4bo37bo4bo2bo3bobo7bo$58b11ob4o5b4ob11o108b2o4bobo6b37o6b
obo4b2o6bobo$55bo12bobo3bo3bo3bobo12bo112bo3b2o41b2o3bo13b2o$48b2o5b6o
b4o3bo3bo5bo3bo3b4ob6o5b2o101b2o5bob43obo5b2o$47bo2bo9bobo3bo5bo7bo5bo
3bobo9bo2bo94b2o3bo2bo4bo45bo4bo2bo$47bo2bo3bob2o3bo3bo6b2o5b2o6bo3bo
3b2obo3bo2bo90bo2bo2bo2bobo6b45o6bobo6b2o2b2o$48b2o4b2o2bo5bo23bo5bo2b
2o4b2o90bobo2b2o4bo3b2o49b2o3bo7b2o2b2o$57bo6b2o3b2o11b2o3b2o6bo100bo
12bob51obo6b2o8b2o$54b3o13bo11bo13b3o110bo53bo6b2o8b2o$54bo6b2o7bobo7b
obo7b2o6bo101b2ob2o5b53o13b2o$50bo4b2o5bo8b2o7b2o8bo5b2o4bo98bobo3bo
57bo10bobo$49bobo4bo5bobo23bobo5bo4bobo97bo2bo2b61o5b2obobo$49bobo3bo
7b2o23b2o7bo3bobo93b2o3b2o64bo3bo2bobo$50bo4b2o39b2o4bo93bo2bo4b65o4bo
2bo$195bobo2bo3bo64b2o3b2o$65b2o19b2o106bobob2o5b61o2bo2bo$48b2o14bo2b
o17bo2bo14b2o89bobo10bo57bo3bobo$47bo2bo13bo2bo17bo2bo13bo2bo89b2o13b
53o5b2ob2o$48bobo14b2o19b2o14bobo86b2o8b2o6bo53bo$49bo53bo87b2o8b2o6bo
b51obo12bo$17b3o113b3o57b2o2b2o7bo3b2o49b2o3bo4b2o2bobo$19bo113bo59b2o
2b2o6bobo6b45o6bobo2bo2bo2bo$18bo115bo70bo2bo4bo45bo4bo2bo3b2o$206b2o
5bob43obo5b2o$195b2o13bo3b2o41b2o3bo$194bobo6b2o4bobo6b37o6bobo4b2o$
195bo7bobo3bo2bo4bo37bo4bo2bo3bobo$204bobo3b2o5bob35obo5b2o3bobo39b3o$
205bobo6bo3b2o33b2o3bo6bobo40bo$91b3o112b2o5bobo6b29o6bobo5b2o42bo$91b
o121bo2bo4bo29bo4bo2bo$65b2o25bo121b2o5bob27obo5b2o$64bobo89bo48bo12bo
3b2o25b2o3bo12bo$3o63bo83b3o3b2o47bo11bobo6b21o6bobo11bo39bo3b2o$2bo
147bo4bobo47bo11bo2bo4bo21bo4bo2bo11bo38b2o3bobo$bo149bo66b2o5bob19obo
5b2o51bobo2bo$21b2o107b2o82b2o7bobobo17bobobo7b2o$22b2o105b2o82bobo6bo
bo5b13o5bobo6bobo$21bo28b3o44b3o31bo80bobo6bobo5bo13bo5bobo6bobo$52bo
44bo115bo7b2o6bob11obo6b2o7bo$32bo18bo46bo21bo106bobobo9bobobo$32b2o
85b2o88bo16bobo3b9o3bobo16bo$31bobo85bobo86bobo11b2o2b2o8bo8b2o2b2o11b
obo$40bo60bo10bo96b2o10bobo8b2o5b2o8bobo10b2o$40b2o58b2o9b2o109bo8bobo
5bobo8bo$39bobo58bobo8bobo118bo7bo$161b3o69b3ob3o$156b3o4bo55b2o14bobo
14b2o$19b2o111b2o24bo3bo3b3o49bobo11bobo3bobo11bobo$20b2o109b2o24bo10b
o49b2o10b3ob2ob2ob3o10b2o49bo$19bo113bo33bo61bo13bo59b2o$171b3o54bobo
11bobo58bobo$173bo55bo13bo55b2o$172bo4bo117bo3bobo$177b2o115b2o3bo$
176bobo115bobo$302b2o$302bobo$185bo101bo14bo$178b3o4b2o99b2o4b3o$15b2o
119b2o42bo3bobo99bobo3bo$16b2o117b2o42bo113bo$15bo121bo3$183bo105bo$
183b2o6b3o85b3o6b2o$182bobo8bo85bo8bobo$192bo87bo$170b2o129b2o$169bobo
129bobo$171bo129bo$182b2o16b3o67b3o16b2o$181bobo18bo67bo18bobo$183bo3b
2o12bo69bo12b2o3bo$188b2o5bo81bo5b2o$187bo7b2o79b2o7bo$194bobo79bobo$
201b2o56b2o3b2o4b2o$183bo16bobo56bobo2bobo3bobo16bo$183b2o8b2o7bo56bo
4bo5bo7b2o8b2o$182bobo7bobo83bobo7bobo$194bo14bo68bo$209b2o$199bo8bobo
62bo$199b2o61b2o8b2o$198bobo61bobo7bobo$191b2o69bo17b2o$192b2o85b2o$
191bo89bo!

Really before any actual recipe construction gets started, the first research item will be to see how much smaller the initial constellation can be, and how much cheaper the activation can be made.

The spacefiller's south end is a mirrored copy of the north end, of course, but we can't use quite the same recipes that were used in the greyship synthesis, since those start with the north end and work downward. "Meet in the middle" isn't an option for glider constructions, so it seems it will be necessary to invent different construction tricks for the south end.

Possibly those tricks will end up getting used to start with a long thin structure along the equator, and then use the same recipe to build toward both ends. Or possibly not -- there might not be much reason to re-think the first half of the greyship recipe. I'm definitely not any kind of expert on the details of this synthesis problem.

Stable Pseudo-Heisenburp for c/3 Spaceships
David Bell suggested a project involving the newly constructible "crotchet" extensions for c/3 spaceships. The result was a stable pseudo-Heisenburp device for crotchets, along with a way to string together crotchet adder components to build c/3 spaceships of any size.

Discoveries and Optimizations
There's been quite a bit of work, off and on, optimizing glider syntheses of still lifes. With the appearance of a long-awaited six-glider synthesis of the "amphisbaena" still life, it is now known that all still lifes with eleven cells or less can be constructed with <=6 gliders:

Code: Select all

x = 33, y = 26, rule = B3/S23
32bo$30b2o$31b2o6$7bo$5bobo$6b2o2$10bo$10bobo$2bo7b2o$3b2o$2b2o$8bo$6b
2o$7b2o4$bo$b2o$obo!

Another record-keeping item is that Catagolue is very close to having collected at least one SHA-256 preimage for a 16x16 soup that produces every possible still life up to 15 bits. Only the long^9 snake has never appeared naturally (i.e., produced by a 16x16 asymmetric soup). Oddly, the other longest-term holdout (xs15_321e88gzxca1) showed up for the first time on February 21 ... and then showed up for the second time less than twenty-four hours later.

Another Catagolue result is a new strictly volatile p25 oscillator found in a symmetric soup sent in by Charity Engine:

Code: Select all

x = 37, y = 37, rule = B3/S23
13b3o5b3o3$10bo15bo$9b2o15b2o$10bo2bo9bo2bo$11b2o11b2o3$4bo27bo$3b3o25b
3o$6bo5bob3o3b3obo5bo$6bo4bo3bo5bo3bo4bo$o4bo8bo7bo8bo4bo$o10bobo9bob
o10bo$o10b2o11b2o10bo$11bo13bo4$11bo13bo$o10b2o11b2o10bo$o10bobo9bobo
10bo$o4bo8bo7bo8bo4bo$6bo4bo3bo5bo3bo4bo$6bo5bob3o3b3obo5bo$3b3o25b3o
$4bo27bo3$11b2o11b2o$10bo2bo9bo2bo$9b2o15b2o$10bo15bo3$13b3o5b3o!

Other search methods have turned up other new oscillators, like this p53 found by Mitchell Riley:

Code: Select all

x = 51, y = 36, rule = B3/S23
24bo$24b3o$27bo$26b2o2$29b2o$28bobo$5b2o21b2o$5bo$6b3o$2o6bo$bo6bobo8b
2o3bo$bobo5b2o8b2o2bobo$2b2o18bo$6b2o15bobo$5bobo$5b2o3$44b2o$43bobo$
25bobo15b2o$28bo18b2o$25bobo2b2o8b2o5bobo$26bo3b2o8bobo6bo$42bo6b2o$42b
3o$45bo$21b2o21b2o$20bobo$20b2o2$23b2o$23bo$24b3o$26bo!

Greyships and Knightships
Keith Amling's spaceship discoveries continue, including completed greyships escorting arbitrarily large patches of OWSS agar:

https://conwaylife.com/forums/viewtopic.php?p=156856#p156856
https://conwaylife.com/forums/viewtopic.php?p=157631#p157631
https://conwaylife.com/forums/viewtopic.php?p=157697#p157697
https://conwaylife.com/forums/viewtopic.php?p=156338#p156338

And last but not least, Sir Robin's band of minstrels got a new member on January 20th, with the addition of the surprisingly small "baby minstrel" which can attach to Sir Robin, Sir Sprayer, and other minstrels in over a dozen different ways, as well as to itself.

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #36, 3/14/2023 1:59pm

NewLifeCA #36, 14 March 2023: spacefiller synthesis completed, new glider shifter, new p68 gun

Happy Pi Day!

Spacefiller Synth
-----------------------
The big news from yesterday and today is that, as rumored in NewLifeCA #35, a 2180-glider synthesis of a spacefiller is now known, down from 2283 and then 2263 and then 2219 -- I think -- it's hard to keep up at this stage of optimization. Further reductions are likely.

This will make it fairly easy to complete a 15-glider RCT recipe for a spacefiller... though the Spartan one-glider seed that will be needed for the final "ATBC" stage is about an order of magnitude bigger than any seed that has been assembled up to this point. The seed hasn't been constructed yet, but all of the necessary pieces are known.

With any luck, the existence of this problem will encourage the development of an automatic assembly script for 1-glider seeds for arbitrary incremental syntheses. There are currently some helper scripts that can assist with turning a slow salvo into a seed, or with assembling a closely-packed synchronized salvo. There aren't any theoretical barriers to solving the generalized seed-building problem, but there's no comprehensive script that provides solutions in practice -- let alone reasonably optimized solutions.

Barberpole Breakthrough
In other news, an interesting new growing spaceship turned up in Keith Amling's searches:

Code: Select all

#N c/4 barberpole stretcher attached to known c/5 barberpole eater
#O Keith Amling, 9 March 2023
#C https://conwaylife.com/forums/viewtopic.php?p=158775#p158775
x = 86, y = 118, rule = B3/S23
15b2o$15bobo$15bo$18bo$17bobo$17bobo$9b3o5bo$9bo7bo$4b2o6b2o3bo3bo$4bo
bo3bo6bo3b2o$4bo5b2o4bo3bo$7bo4b3o9b2o6b2o$7b2o11bo3bobo3b2obo$18b2obo
11b2o$bo11b2o2bo3bo4bobo3b3o$2o12bo6bo2bo4bo4bo$obo9bo7bo7b2ob2o$4bo5b
2o5b3o10b3o$3bo2bo2b2o2bo3bo3bobo4b2o4bo$3bo3bo2bo5bo4bobo4b2o3b2o$7b
5o7bobo5bobo3b3o$9bo6bo2bo7bob2o3bo$6bobo6b2ob4o6b4ob2o$5bo8b2obo2b2o
7b2obobo$4b2o2bo4b2o5b2o8bobob3o$3bo10bo5b2o13bo2bo$3bobob2o6b2o3b2o8b
3o2bo3bo$4bo2b2o4bob2o14b2o2b2obo$7b3o2b5o6bo12bo$12bo6b2ob2o10b3o$12b
ob2obo2bo13b3o$17bo3bo15bobo$11b2o7b2obo9b2o$7b2o3bo2b4ob2o2bo8b3o$7bo
bo2b2obo7b3o9bob2o$7bo6b2o2b3o2b2o12b2o$10bo3b3o5b3o8b2o$10b3ob2o7bo9b
2o2b2o$14bobobo3bo9bo2bo2bo$16b2o4bo2bo6b4ob2o$10b3o3bobo2b2obo9bobo$
10b3o4bobo2bo$5b3o10bo3b2o8bobo$5bo2b3o8bo11bo3bo$8bo21b2ob4o$5bo2bo
24bob6o$5bo2bo3bo23b2o4bo$6b2o2b2obo19b2o7bo$6bo7bo18b2o2b2o$7bobo23b
2o2b2o$7bobo4bo24b2o2bo$11b5o21bo3b2o$14b2o$37b2obo$10b3o25bo2b2o$10b
3o25bo4bo$42b2o$9b2o27bob4o$9bo28bo2b2o$38bo4bo$39b2obo2$40b3o$38b2ob
3o$37b2o4bo$37bobob2o$42bobo$37bo4bobo$36bobo2b3o$36bo2bo2bo2$38b2o$
40bobo$39b2ob2o$40bob2o$43b2obo$43bo2bo4bo$43bo2b2ob4o$42b3o3bo4bo$43b
2o2bo2b2o3bo$44bob4o2b2obo$44b2ob2obo$45bobo2b3o$47b2obo2bo$46b3o4bob
2o$47b2o3b2o2$53bob2o$52bo4bo$51b2o2b3o$54bo2bo$54b3o$55b2o$58b2obo$
61b4o$58bo2b3o$59bo$60bo2$61b2o$61b3o$62bobo$63bo$63b3o$65b3o$66b2o$
66b2obo$69b3o3bo$69b2obobobo$74bobo$67b3o5bo$67bo7b2o$68b2o5bo5bo$74bo
3b3o2bo$75bo2bo4bo$81b2ob2o$83bo$84b2o!

He also started a new thread documenting search results on waves of various speeds, widths, and symmetries. Search results are documented here.

Glider shifter
Unlike the known color-changing Bandersnatch, this new glider shifter is color-preserving, shifting a glider sideways by eight lanes and delaying it by two ticks ( mod 8 ).

Code: Select all

#N bi-block 8hd glider shifter
#O Mitchell Riley, 9 March 2023
#C Repeat time is 59 ticks.
#C https://conwaylife.com/forums/viewtopic.php?p=158774#p158774
x = 29, y = 32, rule = B3/S23
21b2o$5bo15b2o$6bo8b2o$4b3o7bobo2b4o$14bobobo4bo$15bobobobobo$17bobob
2o4b2o$16bobo8bo$17bo7bobo$2bo22b2o$bobo$o2bo$2ob2o$bo4bo$o2b4o5b2ob2o
$b2o9b2ob2o$3b2o$3bo$4bo$b3o$bo4$8b2o$8bo2bob2o$9b3obobo$13bobo2bo$11b
3ob4o$10bo3bo$10b2o2bobo$15b2o!

It's fairly clear that this new discovery will eventually help reduce a bounding box here and there -- e.g., you can't get that lane offset with just two Snarks, and you can't get that change in timing with any number of Snarks -- but it's kind of a specialty mechanism, so it may take a while to find where exactly it belongs.

At the moment it's a very nice solution looking for a problem -- so if you have such a problem, please share it.

Hasslers
In the New Oscillator Engines department, here's a record-breaking period 68 gun:

Code: Select all

#N p68 glider gun
#O iNoMed, 6 March 2023
#C right side sparker optimized by Matthias Merzenich
#C https://conwaylife.com/forums/viewtopic.php?p=158651#p158651
x = 39, y = 33, rule = B3/S23
15b2o$16bo$16bob2o3b2o$17bobo4bo$6b2o11bob3o10b2ob2o$7bo10b2obo13bobo$
7bobo23bobo2bo$8b2o22b3ob3o$32b2o$13b3o16bo2bob2o$22b2o11bo2bo$11b2o2b
ob2o2b4o8bobobo$10bobobo4b2o4bo8b2ob2o$9b5o5bo2b4o8bo$2o6b6o12b2o7b4o$
bo5b2o2b2o2bo3bobo4bobo9bo$bobo3bo5bo2b4o2bo5bo8bo$2b2o3bobo4bobo3bo2b
2o2b2o8b2o$8b2o12b6o$10b4o2bo5b5o$10bo4b2o4bobobo$11b4o2b2obo2b2o$12b
2o$20b3o15bo$36bobo$26b2o9b2o$26bobo$14bob2o10bo$12b3obo11b2o$11bo4bob
o$11b2o3b2obo$19bo$19b2o!

It looks like the search that turned up this gun is part of a larger effort by David Raucci and others, to catalogue partial results for these types of oscillator engines and complete them where possible. For anyone who might want to dig a little deeper into this topic, the current fringes of hassler research can be seen in places like this.

The common active reaction on the second row, marked as 16361 // 68, is the one that iNoMed was able to complete into a gun, by supplying the missing sparks. It's two symmetric copies of a commonly seen sabotaged R-pentomino descendant. The "16361" is the count for that object from Simon Ekström's census.rle.

Code: Select all

#C See also
#C   https://conwaylife.com/forums/viewtopic.php?f=2&t=2656
x = 25, y = 30, rule = B3/S23
23bo2$21b2obo$21bo$21b3o14$9bobo$7bo5bo2$13bo7bo$2bo17bobo$9bobo8bo2bo
$obobo15bo2bo$13bo7bobo$2bo18b2o$13bo$7bo$9bobo!

The searches that find these kinds of partials are basically period-agnostic, and are being done partly with the hope of stumbling over a completable period-19 or period-41 engine sooner or later. But of course it's a lot easier to find completions when the period happens to have a small divisor, because that way the ever-larger custom sparker toolkit can be applied to the problem.

Life Lexicon
There's been just a bit more interest recently in patching up the last few years' worth of gaps in the Life Lexicon. Further contributions made in this forum thread would be greatly appreciated!

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #37, 4/6/2023 11:49pm

NewLifeCA #37, 6 April 2023: strange spaceships and odd oscillators

New Oscillators
April 1 was an unusually prolific day for interesting new oscillator engines. Let's start with this highly improbable-looking construction:

Code: Select all

#N 72P119
#O Mitchell Riley, 1 April 2023
#C https://conwaylife.com/wiki/72P119
x = 51, y = 32, rule = B3/S23
24b2o$24b2o$19bo$17b3o$16bo25b2o$16b2o24b2o2$34b2ob2o$2b2o30bo2bo$2b2o
30bobobo$36b5o$25bo13b2o$24b3o11b3o$23b2ob2o19b2o$22b3ob3o18bobo$2o20b
3ob3o20bo$bo20b3ob3o20b2o$bobo18b3ob3o$2b2o19b2ob2o$10b3o11b3o$10b2o
13bo$10b5o$12bobobo30b2o$13bo2bo30b2o$12b2ob2o2$7b2o24b2o$7b2o25bo$31b
3o$31bo$25b2o$25b2o!

Maybe rephasing a pentadecathlon isn't all *that* unlikely, but it certainly looks impressive. It's currently SKOP 119 (Smallest Known Oscillator of Period 119).

A blinker factory / rephasable block keeper found on the same day produced SKOP 128, 192, 256, and 384, and then today a record-breaking smallest period-960 gun found by MathAndCode:

Code: Select all

#N 51P384 and derivatives
#O Mitchell Riley, 1 April 2023
#C https://conwaylife.com/wiki/51P384
#C counterclockwise from northeast:
#C suppressed p64 (not a SKOP), p 128, p192, p256, p384, p960 gun
#C ( https://conwaylife.com/forums/viewtopic.php?p=160174#p160174 )
x = 126, y = 81, rule = B3/S23
48b2o$48bo$31b2o13bobo22b2o$21b2o8b2o13b2o13b2o8b2o$22bo39bo$21bo39bo
22b2o$21b2o38b2o21b2o$23bo5b3o31bo5b3o$21b3o37b3o$20bo39bo$20b2o38b2o
2$36b2o10b2o26b2o10b2o$30b2obo2bo12bo20b2obo2bo12bo$34bo11b3o25bo11b3o
$31b2o13bo24b2o13bo$24b2o3bo2bo14b2o15b2o3bo2bo14b2o$24b2o3bo2bo15bo
15b2o3bo2bo15bo$31bo15bo23bo15bo$37b2o8b2o28b2o8b2o19b2o11b2o$37b2o38b
2o30bo11bo$108bo13bo$108b2o5bo5b2o$111b2obobob2o$106b5obobobobob5o$
105bo4bo3bobo3bo4bo$106b3ob2o2bobo2b2ob3o$108bo5bobo5bo2$109bo3bo3bo3b
o$111bo7bo2$11b2o78b2o$b2o8b2o68b2o8b2o$2bo79bo$bo22b2o55bo$b2o21b2o
55b2o$3bo5b3o71bo5b3o$b3o77b3o$o79bo$2o78b2o2$16b2o10b2o66b2o10b2o$10b
2obo2bo12bo60b2obo2bo12bo$14bo11b3o65bo11b3o$11b2o13bo11b3o50b2o13bo$
9bo2bo14b2o8bo46b2o3bo2bo14b2o$9bo2bo15bo8bo3bo42b2o3bo2bo15bo$11bo15b
o9bo2bobo48bo15bo$17b2o8b2o10bobo2bo52b2o8b2o$17b2o21bo3bo52b2o$44bo$
41b3o2$37bo$36bobo$37bo3b2o3b2o$40b2o4b2o$40b2o$40b3o$41b2o2$31b2o38b
2o$21b2o8b2o28b2o8b2o$22bo21bo17bo$21bo21bobo15bo$21b2o21bo16b2o$23bo
5b3o31bo5b3o$21b3o37b3o$20bo39bo$20b2o38b2o2$36b2o10b2o26b2o10b2o$30b
2obo2bo12bo20b2obo2bo12bo$34bo11b3o25bo11b3o$31b2o13bo24b2o13bo$24b2o
3bo2bo14b2o20bo2bo14b2o$24b2o3bo2bo15bo20bo2bo15bo$31bo15bo23bo15bo$
37b2o8b2o28b2o8b2o$37b2o38b2o!

As usual, this is only a small fraction of the new oscillator engines that have showed up since Pi Day on the Oscillator Discussion Thread -- starting here.

New Spaceships
Building off of a discovery last fall, "Game of Life Fun" has come up with some very odd-looking extensible spaceships and puffers -- new discoveries I believe:

Code: Select all

#N B-heptomino chain wave, spaceships and blinker puffer
#O Game of Life Fan, 28 September 2022 and 5 April 2023
#C https://conwaylife.com/forums/viewtopic.php?p=160150#p160150
x = 134, y = 56, rule = B3/S23
3o$o2bo$o6b3o4b3o$o5bo2bo4bo2bo4bo$bobo2b2obo4bo6b3o$18bo2bob2o$22b3o
26b3o$15b2o5b3o25bo2bo6b3o$bo13b2o5b2o20bo5bo3bo4bo2bo6b3o$3o12b3o25b
3o3b2o2bo5bo3bo4bo2bo6b3o$ob2o11b2o26bob2o3bobobo5b4o7bo5bo2bo6b3o$b3o
10bobo27b3o4b4o7b2o13bo3bo4bo2bo6b3o$b3o4b2o4b2o28b3o5b3o21b2o2bo5bo3b
o4bo2bo6b3o$b2o3bob2o4bo4b3o22b2o25b4o2bobobo5b4o7bo5bo2bo6b3o$7b2o10b
o2bo36bo2bo3bo4b4o3b4o7b2o13bo3bo4bo2bo6b3o5b3o$14bo4bo39bo2bo4b3o2b2o
5b3o21b2o2bo5bo3bo4bo2bo4bo2bo$12b4o3bo3bo37b2o35b4o2bobobo5b4o7bo7bo$
11b5o3bo66bo2bo3bo4b4o3b4o7b2o15bo$10bob2o6bobo63bo2bo4b3o2b2o5b3o21bo
bo$9b3ob2o73b2o35b4o$10bo3bo64bobo31bo2bo3bo4b4o$11b4o65bo32bo2bo4b3o
2b2o$12bo102b2o$106bobo$9b2o96bo$8bo2bo$9b2o8$19bo$18b3o$18bob2o4bo6bo
6bo6bo6bo6bo6bo6bo6bo6bo6bo6bo$19b3o3b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b
3o4b3o4b3o4b3o$19b2o3b2o2bo2bo2b2o2b2o2bo3bob2o2b2o2bo2bo2b2o2b2o2bo2b
o2b2o2b2o2bo3bob2o2b2o2bo2bo2b2o3b3o$24bo3bo2b3o15bo2b2ob2o2bo3bo2bo3b
o2b3o15bo2b2ob2o2bo3bo2bo2bo$24bob2o21b3o3b2o4bobo2bob2o21b3o3b2o4bobo
5bo$24b2o23b3obob2o9b2o23b3obob2o8bo3bo$18b3o28bob2o2bo2b2ob2o28bob2o
2bo2b2ob2o6bo$17bo2bo20b2o5b2obo3bo4bo22b2o5b2obo3bo4bo5bobo$20bo19b3o
5bo3bobo27b3o5bo3bobo$16bo3bo14b2o11bo4bo23b2o11bo4bo$20bo12bo5bobo3b
3o27bo5bobo3b3o$17bobo11b2o5b2o26b2o5b2o5b2o26bo$30bo8b2o12bo5b2o5b2o
4bo8b2o24b3o$31b2o18b3o4bob2o3bo7b2o32bob2o$32bo17bo2b2o2b2ob2o3bobo6b
o22b2o9b3o$42bo2bo3bo2bo5bob2o4b2o28bo2bo8b3o$35bo6bo3bo3bo2b2o4b2o36b
2o9b2o$28bo6bo6bo2bo5b3o$28bo6bo17bo$28bo!

They're very similar to some of the weird wave patterns created by GUYUT6J and praosylen and others, where there is an illusion of sideways motion along the chain, but the movement is much faster than the speed of light -- see, e.g., here and here.

Keith Amling has completed a single-line c/5 linestretcher, to go along with the c/5 single-line back end that was found previously.

Code: Select all

#N c/5 diagonal line stretcher
#O Keith Amling, 3 April 2023
#C Improved by Matthias Merzenich, 4 April 2023
#C https://conwaylife.com/forums/viewtopic.php?p=160125#p160048
#C A matching c/5 diagonal line-eater was completed on March 29:
#C https://conwaylife.com/forums/viewtopic.php?p=159774#p159774
x = 96, y = 99, rule = B3/S23
93b2o$91b2o2bo$91b3o$91bobo$87b4o2bo$87b3o3bo$89bob2o$88bo6bo$88b2o4bo
$90b3o$86b2o$85bo2b2o$84b2o2bob2o$83bo4bobobo$83bo5b2obo$83bo2b2ob2o$
85b2o2b2o$88bo$90bo$87bo2bo$86bo$85bo2b2o$84bo$83bo2bo$83bo2$82b2o$82b
o2bob2o$87bo$74b3o$73bo9b2o2bobobo$72bo3bo5bo2b3obo2bo$72bob2o6bo2b3o$
72bo2bo6bo$60b2o2bo8b2ob3o2bo4b3o2bo$39bo6b3o8b4o3b2o7b2o4bo2bo4bob2o$
39b2o4b2o14b2o2bo3b2o3bobo7bo$35b2o2b3o3b6o5bo2bo5b2o3b2o4bob2o$34b2ob
o3b3o4bo3bo3bo2bo6bob2o15b2o$21b2o8b2o2bob2o4bo5bo2bo2b2ob2o6b3o17bo$
20b3o5b2obo3bo2bo2bobo3bo8bobo24bo3bo$19b2o7bo2bobo10b4o2bo3b2o26b2ob
2o$18b3ob2o5bo2b3ob2o7bobo2bo3bo29bo3bo$14b2obo3b2o5b2o3bo2b2obo6bo2b
2o3bobo27b5o3bo$14bo6bo14b3obo8b2o4b2o28bo3bo2b2o$14bo2bo7b2o3bo9bo3b
3o3bo4bobo28b3o3b2o$14bo4b2o4bo6b3ob3o17b3o29bo$12b5o2b2o5bo6b2o23b4o
26bo$11bo5b3o5b2o33b3o25b2o$10bo2b4o43bo2bo27b2o$10bo2bobobo2bo41b2o
24bo$9bo2bo50b2o22bo4bo$10b2o3b3o45b3o22b4o$10b2o4bob2o43bo$10b2o5b3o
44b2o$4b3o2b2obo6bo67b3o$3bo3b6o4b2o67bobo$3bo2bob2o6bo2bo65b2o2b3o$2b
obob4o7bob2o68b2o$bobobo2b3o5b2ob2o68b2o$o5bo9b2obo$ob4o15bo$ob3o11bo
4bo$17bo$20b2obo$23bo$20bo2bo$20b2o$20b3ob2o$22bobo2bo$25bo$27b3o$28b
2o2$29bobo$31bo$30bobobo$30b5o$30b2o$29b3o5bo$27b2o6b5o$27b3o4b2o3b2o$
37bob2o$34b2o5bo$34b2ob2o2bo$34b2ob2o3b2o$33bo5bobo$34bo$36bobo$38b5o$
39b2ob2o$42bobo3bo$41bo2b2ob5o$47bo5bo$47b4o2b3o$53bo$52bo$51bo$52b2o!

This is the latest in a series of new results from Keith Amling and Hartmut Holzwart, many of them from a survey of the space of extensible wave patterns within reach of current search technology, from this thread.

Maybe a special callout is warranted for "the most wretched agarship...", escorting long skinny patches of a high-density p2 agar.

A c/5 orthogonal antstretcher has also appeared.

Spacefillers
Also from Keith Amling, with adjustments by Matthias Merzenich and AlbertArmstain, here's an impressive new Quartermax:

Code: Select all

#N new-quartermax
#O Keith Amling, Matthias Merzenich, AlbertArmstain 22-23 March 2023
#C https://conwaylife.com/forums/viewtopic.php?p=159493#p159493
x = 83, y = 75, rule = B3/S23
46bo$45b3o$45bob2o$46b3o3b3o$46b3o3bo2bo$46b3o2b2o3bo$46b2o8bo$54bo$
55bobo$51b3obob2o$51bo3bobobo12bo$57bob2o7b2ob3o$50b2o5bo3bo4b2obo3b2o
$66bo4bo2b2o$28bo28b2ob2o3b2obo5bo$14bo12b3o33b2obo7b2o$13b3o5b3o2bo2b
2o24b8obo7bobob2o$12b2obo4bo2bo2b5o22b2obo5bobob2o3b2obobo$12b3o9bob2o
2bo14b3o4bo9bobo5bo3bobob2o$12b3o7bobobo4bo12bo2bo3bo3bo3bo4bo9bo3b2o$
12b3o3b3obobobo2bo2bo14bo3bo3bo14b2o3bob3o$13b2o4bo3b2obo2bo17bo2b2obo
4b2o19b2o$17bobo5bobo4b2o10b6obob2o2bo2bo$30bo3b2o3bo5bo2b2obo3bo20bo$
20b2o9b2obo2b2ob2ob5o2b5ob2obo15b3o$19b3o14bobob2ob2obo8b3obo14b3ob2o$
19b2o10b5ob2o3bo4b2ob6o2b2o2bo4bo4b2obo2bo$30bo8b3o4bo7b2o2bo2b3ob2ob
2obobo4bob2o$30b5ob3o4bobobo3bo7b5o7bobo2bobob2o$12bobo13bo5bobo2b3o3b
ob5o6b2o3b2obobob3o8bo$11bo2bo13b6o2bobo2b4o2bobo22b2o7b2o$10b2o14bo6b
obo2b2ob2o4bobo$9bo3bo12b7o2bobo5b3ob2o$8b3obo11bo8b3o2b3o6bobo$5b2o
17b9o3bo7b2obob2o$4bo3b5o9bo11bo4bobo3bobobobo$3bo3bo14b15ob2ob2o2bobo
bob2o$3bo5b2o9bo18bo3bobobobobobo$3b3o3b4obo5b16obo2b4obobobobob2o$5bo
6b2obo2bo17b2obo5bobobobobobo$14b2o2b17o4bob2obo2bobobo3b2o$15b2o18b3o
bob2ob2obobobobo3bo$2b4o10b19o3bo8bobo4bo$b6o29bo10bob2o5b2o$2ob4o7b
27o3b2obobo$b2o10b2o26bo2b2obob2o$12b2o2b3o2b4o2b4o2b4ob4o5bo7b3o$11b
3o2b3obo2b2obo2b2obo2b2o5b4obo2bo3bo2bo$12bobo7bo5bo5bo5bo4bobo3bo5bo$
13b3o25bobo3bobobo5bo$12bo2b2o24bob2o2bobo2b2o2bo$15b3o2bo21bo2bobobo
4bo$15b3o2bo21bobo2bobo2bob3o$9b2o7bo17b2o3b3o3bob3obob2o$8b2ob5ob2o
16bo10b2ob2o3b2o5b3o$9b6ob3obo13bobo2bob3o3bo8b2o2bo2bo$10b3o3bo2b3obo
b2o7bobo7bo2bo2bo2bo4bo4bo$18b2obob2o8b2obob2o2b2obobobo3bo9bo$16bo9b
2o7bob2o4bobobobobo5b2o4bo$14b2o2bob3obo2bob2o4bo3b4o2bobob2o3b3o3bobo
$14bo4bo2bobob2ob2o5b2obo2bobo2bob2o$14bo3b2o5b3obo8bo5b2obo11bo$15b3o
7b2o11bobo3bo2bo2bo7bobob2o$39b2o5b2obo7bo2bobo2b2o$47bobobo4bob3o2bob
o$47bob2o6bo3b3obo$46b2ob2o7b2o4bo$47bo14b2o$47bobob2o6bo2bo$48b2ob2ob
obo2b2obo$50bo3bobobobob2o$50bob2o2bobob2o2bo$51bo2b2o3bo3b2o$53bo6b3o
$52b2o8bo!

In other spacefiller news, Goldtiger997's spacefiller synthesis recipe has gotten boiled down to 1115 gliders now.

Work is in progress on converting that 340-stage recipe into a constructible seed pattern. A spacefiller is a particularly appropriate pattern for a 15-glider reverse caber tosser mechanism to build, but a seed triggerable by a single glider will be needed.

RCT15 is particularly appropriate because all of its machinery conveniently cleans itself up anyway, before completing the construction of its target object. If most other types of universal constructor attempted to build a spacefiller, the results would be ... spectacular, but messy.

More soon?
Some kind of follow-up is likely in the next few days. I'm sure I've accidentally left out some good stuff as usual. Keep the cheer,


Dave

NewLifeCA #37 response on forums

Also from Keith Amling, with adjustments by Matthias Merzenich and AlbertArmstain, here's an impressive new Quartermax:

It's important to note in any follow-up that Keith Amling was completing a quartermax design - using a p5 wick allowing a switch from horizontal to vertical stripes with a 2c/4 stretcher (rather than using a direct 4c/8 stretcher as in the previous quartermax) - that was proposed by Hartmut Holzwart several years ago. I would consider Amling and Holzwart as co-discoverers in this case.

This probably is not worth mentioning (don't want to clutter with unnecessary minor differences), but I also posted a slight bounding box reduction to this quartermax which uses some improved components over the version shown in NewLifeCA #37.

As for things that are missing, there is the first engine-based p61 gun, representing a significant reduction for that period:

Code: Select all

#N Engine-based period-61 gun
#O Mitchell Riley, 5 April 2023
#C https://conwaylife.com/forums/viewtopic.php?p=160181#p160181
x = 48, y = 44, rule = B3/S23
7bob2o$7b2obo2$5b5o4b2o$4bo4bo5bo$3bo2bo8bob2ob2o$3bob2o9bobobo2bo$2ob
o5bo7bo4b2o$bobo4bobo$o2b2o2bo2bo14b2o$2o6b2o15bo8bo$23bobo7bobo$23b2o
8bob3o$30b2obo4bo$30bobobobobo$32bobob2o4b2o$31bobo8bo$32bo7bobo$16bo
23b2o$15b3o12bo$14b2ob2o10b3o$13b3ob3o8b2ob2o$4b2o8b2ob2o8b3ob3o$4b2o
9b3o10b2ob2o$16bo12b3o$30bo$14bo$13bobo$9b2obobo$8bobobobobo30bo$8bo4b
ob2o28bobo$9b3obo8b2o22b2o$11bobo7bobo$12bo8bo15b2o$20b2o14bo2bo2b2o$
36bobo4bo$23b2o4bo7bo5bob2o$23bo2bobobo9b2obobo$25b2ob2obo8bo2bo2bo$
31bo5bo4bo2b2o$31b2o4b5o2$39b2obo$39bob2o!

The following R hassler is the first example of a p42 oscillator whose volatility matches its strict volatility (this was the last composite period for which an example was unknown):

Code: Select all

#N Period-42 R-pentomino hassler
#O Mitchell Riley, 2 April 2023
#C Every cell in this oscillator is either stable or oscillates at
#C the full period. p42 was the last composite period for which no
#C such oscillator was known.
#C https://conwaylife.com/forums/viewtopic.php?p=159973#p159973
x = 29, y = 23, rule = B3/S23
8b2o$7bobo$3b2o2bo$3bobob2o$5bo$5bob2o$ob2obo2bo$2obo2b2o$3bo$3b2o12bo
$17b3o$10bo7bo$9b3o$11bo12b2o$25bo$21b2o2bob2o$20bo2bob2obo$20b2obo$
23bo$20b2obobo$21bo2b2o$19bobo$19b2o!

You might also include the following p47 and p72 5c/9 signal injectors using a known elementary signal-injector by "Rhombic" and Adam P. Goucher:

Code: Select all

#N p47 and p72 5c/9 signal injectors
#O Mitchell Riley, "iNoMed", "Bullet51", 4-6 April 2023
#C New p47 and p72 oscillators give high-period 5c/9 signal
#C injectors using an elementary signal injection reaction
#C found by "Rhombic" and Adam P. Goucher on 3 January 2018.
#C https://conwaylife.com/forums/viewtopic.php?p=160101#p160101
#C https://conwaylife.com/forums/viewtopic.php?p=160166#p160166
#C https://conwaylife.com/forums/viewtopic.php?p=54568#p54568
x = 171, y = 87, rule = B3/S23
12bo4bo$10b3o4b3o$9bo10bo$9b2o8b2o2$7bo14bo$7bo14bo$7bo6b2o6bo$14b2o$
9b3o6b3o$bo26bo$obo4bo5bo2bo5bo4bobo$bo5bo5bo2bo5bo5bo86b2o$7bo5bo2bo
5bo89b2o2bo$9b3o6b3o89b3ob2o$109bo18bo$9b3o6b3o89b3ob2o11b2o$7bo5bo2bo
5bo89bob2o11b2o$bo5bo5bo2bo5bo5bo98bo$obo4bo5bo2bo5bo4bobo$bo26bo$9b3o
6b3o12b2o$14b2o17bobo$7bo6b2o6bo12bo56b2o12b2o$7bo14bo11b2ob2obo52bo
13bo$7bo14bo14bob2o52bob2o10bobo$37bo52b2obo2bo11b2o$9b2o8b2o8b3o4b2o
51bo2bobo24b3o$9bo10bo8bobo57b2obob2o23bobo$10b3o4b3o9bo2bo59bo2bo23bo
2bo$12bo4bo12bobo59b2o26bobo$30b3o87b3o4$40bo56b3o30bo$36b2obobo55bobo
26b2obobo$34bo2bobobo55bo2bo23bo2bobobo$34b2obob2ob2o54bobo23b2obob2ob
2o$35bobo4bo55b3o24bobo4bo$34bo2bob2obo67b2o12bo2bob2obo$31bo2b2obobob
o4bo63bobo8bo2b2obobobo4bo$31b3o3bobo4b3o65bo8b3o3bobo4b3o$34b4ob2o2bo
68b2o10b4ob2o2bo$31b2obo6bo2bo76b2obo6bo2bo$31bobo2b5ob2obo2bo72bobo2b
5ob2obo2bo$34b2o4bobo2b4o75b2o4bobo2b4o$35bo2bo3bobo6bo73bo2bo3bobo6bo
$35bobob4obo2b5o40bo32bobob4obo2b5o$34b2obo6bobo5b2o37b2o11b2obo16b2ob
o6bobo5b2o$37bob4obo2bob2obobo36b2o11b2ob3o17bob4obo2bob2obobo$37bobo
2bob2obobobo2bo36bo18bo16bobo2bob2obobobo2bo$36b2o2bo2bo3bobo4bob2o46b
2ob3o16b2o2bo2bo3bobo4bob2o$38b2o4b4ob2o2b2o2bo45bo2b2o20b2o4b4ob2o2b
2o2bo$38bo3bobo6bo3bo47b2o23bo3bobo6bo3bo$39b4obob2ob2ob3o3bo70b4obob
5ob3o3bo$43bobo2bo3bo2b4o74bobo4bobo2b4o$41bo3bo2bo3bobo6bo69bo3bo2bo
3bobo6bo$41b2o2bobob4obo2b5o69b2o2bobob4obo2b5o$44b2obo6bobo5b2o70b2ob
o6bobo5b2o$47bob4obo2bob2obobo72bob4obo2bob2obobo$47bobo2bob2obobobo2b
o72bobo2bob2obobobo2bo$46b2o2bo2bo3bobo4bob2o68b2o2bo2bo3bobo4bob2o$
48b2o4b4ob2o2b2o2bo70b2o4b4ob2o2b2o2bo$48bo3bobo6bo3bo72bo3bobo6bo3bo$
49b4obob5ob3o3bo70b4obob5ob3o3bo$53bobo4bobo2b4o74bobo4bo4b4o$51bo3bo
2bo3bobo6bo69bo3bo2bo3bobo6bo$51b2o2bobob4obo2b5o69b2o2bobob4obo2b5o$
54b2obo6bobo5b2o70b2obo5b2obo5b2o$57bob4obo2bob2obobo72bob3o2bo2bob2ob
obo$57bobo2bob2obobobo2bo72bobo2bob2obobobo2bo$56b2o2bo2bo3bobo4bob2o
68b2o2bo2bo3bobo4bob2o$58b2o4b4ob2o2b2o2bo70b2o4b4ob2o2b2o2bo$58bo3bob
o6bo3bo72bo3bobo6bo3bo$59b4obob5ob3o3bo70b4obob5ob3o3bo$63bobo4bobo2b
4o74bobo4bobo2b4o$61bo3bo2bo3bobo76bo3bo2bo3bobo$61b2o2bobob4obob3o72b
2o2bobob4obo2b2o$64b2obo6bo4bo74b2obo6bobo2bo$67bob4obo2bo2bo76bob4obo
2bo2bo$67bobo2bob4ob2o76bobo2bob2obob2o$66b2o2bo2bo3bobo76b2o2bo2bo3bo
bo$68b2o4b3o2bo78b2o4b3o2bo$68bo7bobo79bo7bobo$70bo6bo82bo6bo$69b2o88b
2o!

Building off of a discovery last fall, "Game of Life Fan" has come up with some very odd-looking extensible spaceships and puffers -- new discoveries I believe

That should be "Game of Life Fun".

NewLifeCA #37 response via email

Another response this morning, this one from Noam Elkies, gives me
space here for another quick reminder.

Discussion of NewLifeCA news items can perfectly well be sent as a
direct response to the email in question, like the message below.
Responses can also be posted on the discussion thread set up for the
purpose -- if you have a conwaylife.com forum account, or are willing
to set one up:

viewtopic.php?f=7&t=5651

In some cases I may forward either type of message to the email list,
or make a combined digest of responses -- whatever seems reasonable.

-- Dave

Date: Fri, Apr 7, 2023 at 10:00 AM
Subject: Re: NewLifeCA #37, 6 April 2023: strange spaceships and
oddball oscillators

New Oscillators
---------------------
April 1 was an unusually prolific day for interesting new oscillator
engines. Let's start with this highly improbable-looking
construction:

#N 72P119
#O Mitchell Riley, 1 April 2023
#C https://conwaylife.com/wiki/72P119
[ . . . ]
> Maybe rephasing a pentadecathlon isn't all *that* unlikely, but it
> certainly looks impressive. It's currently SKOP 119 (Smallest Known
> Oscillator of Period 119).

This reminds me that way back in April 1, 1995 I posted this:

Subject: p17 "prosofilla"
Date: Sat, 1 Apr 1995 00:06:42 -0500

Code: Select all

  ......oo
   ......oo
   .
   @..o......o..@
   ..o........o
   ..o........o
   ..o........o
   ...o......o
   ......oo

and later explained:

yes, "prosofilla" doesn't work -- after 17 generations the one-bit sparks are missing. It was my attempt at an April fool's joke, as you might have guessed by anagramming its name. Still, if we ever do find a p17 with a one-bit spark this will convert two of them to a domino spark suitable for toad and other reactions.

28 years later we have a few p17's but I don't think any of them can supply the needed spark. Possibly there's some construction of period 15n+2 that supplies both the spark and a transient block (or equivalent spark) that finally makes this work. But it probably wouldn't be as natural as this neat new p119 rephaser (whose period happens to be also a multiple of 17).

NDE

P.S. Many thanks to Dave Greene for keeping us old guard apprised of all those remarkable new B3S23 discoveries!

Dave Greene wrote:

> Building off of a discovery last fall, "Game of Life Fan" has come up
> with some very odd-looking extensible spaceships and puffers -- new
> discoveries I believe:

For what it's worth, I added some random stuff among the blinkers and found this messy reburner. Its speed is 144c/312 (so it never catches up to the front) and converts 73 lines of blinkers into a bunch of junk. There are many variations with the same front end, or with multiple copies of it.

Code: Select all

x = 551, y = 31, rule = B3/S23
547b3o$547bo2bo$8b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b
3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o
4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b
3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o
4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4b3o4bo$2bo4bo2bo4bo2bo2bo2bo
4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo
2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo
2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo
2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo
4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo
2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo2bo
2bo2bo4bo2bo2bo2bo4bo2bo2bo2bo4bo$b3o6bo4bob2o2bo3bo2bo3bo2bo3bo2bo6bo
2bo4bob2o2bo3bo2bo3bo2bo3bo2bo6bo2bo4bob2o2bo3bo2bo3bo2bo3bo2bo6bo2bo
4bob2o2bo3bo2bo3bo2bo3bo2bo6bo2bo4bob2o2bo3bo2bo3bo2bo3bo2bo6bo2bo4bob
2o2bo3bo2bo3bo2bo3bo2bo6bo2bo4bob2o2bo3bo2bo3bo2bo3bo2bo6bo2bo4bob2o2b
o3bo2bo3bo2bo3bo2bo6bo2bo4bob2o2bo3bo2bo3bo2bo3bo2bo6bo2bo4bob2o2bo3bo
2bo3bo2bo3bo2bo6bo2bo4bob2o2bo3bo2bo3bo2bo3bo2bo6bo2bo4bob2o2bo3bo2bo
3bo2bo3bo2bo6bo2bo4bob2o2bo3bo2bo3bo2bo3bo4bobo$2obo2bo15b4o2bobob4o2b
o2bo3bo18b4o2bobob4o2bo2bo3bo18b4o2bobob4o2bo2bo3bo18b4o2bobob4o2bo2bo
3bo18b4o2bobob4o2bo2bo3bo18b4o2bobob4o2bo2bo3bo18b4o2bobob4o2bo2bo3bo
18b4o2bobob4o2bo2bo3bo18b4o2bobob4o2bo2bo3bo18b4o2bobob4o2bo2bo3bo18b
4o2bobob4o2bo2bo3bo18b4o2bobob4o2bo2bo3bo18b4o2bobob4o2bobo$3o21bo4b2o
b2o2bo4bo3bo4bo15bo4b2ob2o2bo4bo3bo4bo15bo4b2ob2o2bo4bo3bo4bo15bo4b2ob
2o2bo4bo3bo4bo15bo4b2ob2o2bo4bo3bo4bo15bo4b2ob2o2bo4bo3bo4bo15bo4b2ob
2o2bo4bo3bo4bo15bo4b2ob2o2bo4bo3bo4bo15bo4b2ob2o2bo4bo3bo4bo15bo4b2ob
2o2bo4bo3bo4bo15bo4b2ob2o2bo4bo3bo4bo15bo4b2ob2o2bo4bo3bo4bo15bo4b2ob
2o2bo$3o5b2o20b3o4b2o2bo8bo21b3o4b2o2bo8bo21b3o4b2o2bo8bo21b3o4b2o2bo
8bo21b3o4b2o2bo8bo21b3o4b2o2bo8bo21b3o4b2o2bo8bo21b3o4b2o2bo8bo21b3o4b
2o2bo8bo21b3o4b2o2bo8bo21b3o4b2o2bo8bo21b3o4b2o2bo8bo21b3o4b2obo3bo$b
2o5b2o27b3o3bo35b3o3bo35b3o3bo35b3o3bo35b3o3bo35b3o3bo35b3o3bo35b3o3bo
35b3o3bo35b3o3bo35b3o3bo35b3o3bo35b3o3b3o$7b3o4bobo20b3o3b3obob2o5bobo
20b3o3b3obob2o5bobo20b3o3b3obob2o5bobo20b3o3b3obob2o5bobo20b3o3b3obob
2o5bobo20b3o3b3obob2o5bobo20b3o3b3obob2o5bobo20b3o3b3obob2o5bobo20b3o
3b3obob2o5bobo20b3o3b3obob2o5bobo20b3o3b3obob2o5bobo20b3o3b3obob2o5bob
o20b3o3bob2o$8b2o4bobo27b3o3b2o4bobo27b3o3b2o4bobo27b3o3b2o4bobo27b3o
3b2o4bobo27b3o3b2o4bobo27b3o3b2o4bobo27b3o3b2o4bobo27b3o3b2o4bobo27b3o
3b2o4bobo27b3o3b2o4bobo27b3o3b2o4bobo27b3o3b2o4bobo27b3o$8bobo3bo30bo
4bobo3bo30bo4bobo3bo30bo4bobo3bo30bo4bobo3bo30bo4bobo3bo30bo4bobo3bo
30bo4bobo3bo30bo4bobo3bo30bo4bobo3bo30bo4bobo3bo30bo4bobo3bo30bo4bobo
3bo29b3o$9b2o5b3o5bo26b2o5b3o5bo26b2o5b3o5bo26b2o5b3o5bo26b2o5b3o5bo
26b2o5b3o5bo26b2o5b3o5bo26b2o5b3o5bo26b2o5b3o5bo26b2o5b3o5bo26b2o5b3o
5bo26b2o5b3o5bo26b2o5b3o5bo19b2o$3b3o4bo7bo5b2o5b2o19bo7bo5b2o5b2o19bo
7bo5b2o5b2o19bo7bo5b2o5b2o19bo7bo5b2o5b2o19bo7bo5b2o5b2o19bo7bo5b2o5b
2o19bo7bo5b2o5b2o19bo7bo5b2o5b2o19bo7bo5b2o5b2o19bo7bo5b2o5b2o19bo7bo
5b2o5b2o19bo7bo5b2o5b2o$2bo2bo10b3o7bo4bobo3b3o5bo12b3o7bo4bobo3b3o5bo
12b3o7bo4bobo3b3o5bo12b3o7bo4bobo3b3o5bo12b3o7bo4bobo3b3o5bo12b3o7bo4b
obo3b3o5bo12b3o7bo4bobo3b3o5bo12b3o7bo4bobo3b3o5bo12b3o7bo4bobo3b3o5bo
12b3o7bo4bobo3b3o5bo12b3o7bo4bobo3b3o5bo12b3o7bo4bobo3b3o5bo12b3o7bo4b
obo$5bo4bo13b2o5bobo6b2o5bo18b2o5bobo6b2o5bo18b2o5bobo6b2o5bo18b2o5bob
o6b2o5bo18b2o5bobo6b2o5bo18b2o5bobo6b2o5bo18b2o5bobo6b2o5bo18b2o5bobo
6b2o5bo18b2o5bobo6b2o5bo18b2o5bobo6b2o5bo18b2o5bobo6b2o5bo18b2o5bobo6b
2o5bo18b2o5bobo$bo3bo3b4o11b2o5bobo2bo3b2o2bo3bo17b2o5bobo2bo3b2o2bo3b
o17b2o5bobo2bo3b2o2bo3bo17b2o5bobo2bo3b2o2bo3bo17b2o5bobo2bo3b2o2bo3bo
17b2o5bobo2bo3b2o2bo3bo17b2o5bobo2bo3b2o2bo3bo17b2o5bobo2bo3b2o2bo3bo
17b2o5bobo2bo3b2o2bo3bo17b2o5bobo2bo3b2o2bo3bo17b2o5bobo2bo3b2o2bo3bo
17b2o5bobo2bo3b2o2bo3bo17b2o5bobo$5bo3b5o17b2o7b2o4b4o23b2o7b2o4b4o23b
2o7b2o4b4o23b2o7b2o4b4o23b2o7b2o4b4o23b2o7b2o4b4o23b2o7b2o4b4o23b2o7b
2o4b4o23b2o7b2o4b4o23b2o7b2o4b4o23b2o7b2o4b4o23b2o7b2o4b4o23b2o$2bobo
6b2obo22b3o4bo3bo30b3o4bo3bo6b3o21b3o4bo3bo30b3o4bo3bo30b3o4bo3bo30b3o
4bo3bo30b3o4bo3bo30b3o4bo3bo30b3o4bo3bo30b3o4bo3bo30b3o4bo3bo30b3o4bo
3bo$10b2ob3o31bo41bo14b3o24bo41bo41bo41bo41bo41bo41bo41bo41bo41bo$10bo
3bo30bo41bo23b3o15bo41bo41bo41bo41bo41bo41bo41bo41bo41bo$10b4o104b3o$
12bo2$14b2o81b3o4b3o$13bo2bo87bobo$14b2o88b3o4b3o$118b3o3$97b3o!

[dvgrn]

NewLifeCA #38, 6/24/2023 11:59am

NewLifeCA #38, 24 June 2023: some surprising spaceships, a new Garden of Eden result, and more

It's been a couple of months already since the last NewLifeCA bulletin.  Time to get caught up, at least on the bigger items!

Stable Storage Spaceship
Engineered spaceships from the original Gemini up until now have almost all encoded construction data in streams of gliders or spaceships.  Some of these, like the "self-synthesizing spaceship", consist of nothing but gliders at some phase of their evolution.  The Stable Storage Spaceship is the first example of a spaceship where one phase consists of a single glider colliding with a large still life constellation.

-- We did have a near miss back in 2014, since the original half-baked knightships can be reduced to five gliders hitting a constellation of stationary stuff (still lifes plus a few blinkers).  It wouldn't take much re-engineering to reduce that to a single-glider activation, and it would be much smaller than the Stable Storage Spaceship, of course.

The Caterloopillars are another type of self-supporting spaceship where data is encoded in stationary objects.  The Stable Storage Spaceship, while it does much more complex construction work than an HBK or a Caterloopillar, still also counts as a self-supporting spaceship rather than a fully self-constructing one.  Just like the others, it relies on the existence of a stable constellation that it knows how to move, and that it reads to obtain its construction recipe, but is not able to completely destroy and rebuild.  Also like the HBK, the specific mechanism for moving the stable constellation limits the adjustability of the direction (but not the speed) that the spaceship can travel.

The Stable Storage Spaceship uses a clever shortcut to minimize the amount of complex tape-reading circuitry.  There's a static tape consisting of the presence or absence of boats at regular intervals -- but there's no "read arm" and no separate READ and COPY stage for each cycle.  Instead, a seed is constructed for a mobile "read head" consisting of a paired Corderpuffer and Corderrake, which passes by the boats encoding the construction recipe and moves them by (200,7) while also converting them to gliders on a particular lane, aimed back to the starting point to activate the construction arm.

The construction arm consists of nothing more than a p256 glider gun and a p8 bumper.  It's designed to produce the same glider-pair spacing as the native RCT construction arm, and it turns out that many of the same elbow operations still work, even though the relative timings of the gliders in the pairs is a bit different.  So the Stable Storage Spaceship, like the RCT, relies on the fact that universal construction can be achieved by a long enough series of free choices between sending a singleton glider vs. sending a pair of gliders on lanes separated by 6 half-diagonals, aimed at an elbow object.

(34,7)c/156 spaceship
In early June, Luka Okanishi completed the largest oblique caterpillar design to date, a (34,7)c156 spaceship.  As usual, many people contributed ideas and mechanisms to the design along the way.

The new spaceship appears to be "technically glider constructible" in the sense that it's probably not outside our collective ability to come up with a recipe for it.  But it's also bigger than any other known spaceship, by any reasonable metric -- excluding "unnecessarily extended" spaceships and comparing only let's say the smallest by population or bounding box for each known speed. At 25,013,268 cells the (34,7)c156 spaceship is over twice as big as the Caterpillar by population -- and it has roughly an 8 million by 6 million cell bounding box, so there's pretty much no comparison there.

Unidimensional Spaceship Progress
A while back a workable mechanism was proposed for a 1xN spaceship, where in one phase all of the live cells are in a single row.  Since then quite a bit of progress has been made on the design and optimization, and construction-arm universality has been reached -- in mirror-image copies on both sides of the line, of course:

As with the RCT, the devil is in the details of the cleanup.  There's nothing that we don't know how to do in theory, but working it all out in practice will still take considerable effort.

No 4-Cell-High Gardens of Eden (?)
Andrew Wade has completed a computer-assisted proof with over twenty billion elements, showing that no pattern can be an orphan if the living and dead specified cells are restricted to four consecutive rows -- every such pattern has a parent.

So far I'm not aware of any attempts to independently verify this result.

Odd Traffic Stop
For anyone whose tastes run more toward the mini than the mega, another interesting three-quarters traffic light catalyst, the odd traffic stop showed up in May.  This catalysis rephases the 3/4TL, so it can be used to support oscillators with odd periods -- unlike the regular traffic stop reaction.

Here are a couple of examples -- p75 on the left using a standard eater3, and p79 on the right with an auxiliary loaf, using a smaller catalyst that's often equivalent to eater3:

Code: Select all

x = 128, y = 41, rule = B3/S23
25b2o93b2o$25bobo92bobob2o$26bo84bo10bobo$111b3o7b2obo$114bo9bob2o$90b
o22b2o6b4o2bo$8b2o80b3o28bo3b2o$9bo83bo28b3o$9bobo80b2o13b2o4bo5bo4bo$
10b2o94bo2bo3bo5bo4bobo$107bobo3bo5bo5b2o$108bo$115b3o$27bo15bo76b2o$
26b3o13bobo75bobo$26bobo6b3o3bo3bo47b3o26bo$9b2o25bo4bo3bo50bo10b2o13b
2o$10bo25bo4bo3bo39b3o5b3o$10bobo23bo4bo3bo40b2o19b3o$11b2o23bo4bo3bo
41bo28b2o$15b3o17b3o3bo3bo40b2o28b2o$42bobo41b2o28bo$13bo5bo23bo50b3o
19b2o$13bo5bo88b3o5b3o$13bo5bo60b2o13b2o10bo$9b2o70bo26b3o$4b2o2bo2bo
69bobo$bo2bo4bobo70b2o$obobo5bo7b2o66b3o$bo2bob2o10bo76bo$4bo2bo11b3o
55b2o5bo5bo3bobo$5bo4bo10bo55bobo4bo5bo3bo2bo$6b5o68bo4bo5bo4b2o13b2o$
79b3o28bo$8bo68b2o3bo28b3o$7bobo66bo2b4o6b2o22bo$8bo67b2obo9bo$79bob2o
7b3o$79bobo10bo$78b2obobo$82b2o!

This potentially opens up quite a lot of new search space in the continuing hunt for p19 and p41 oscillators.

Spacefiller Seed
As part of an ongoing rework of the RCT project, Adam P. Goucher has assembled the largest 1-glider seed ever constructed -- largest by about a factor of five, with 3568 objects, where the two runners-up consist of 700-odd objects each.

This seed is likely to be combined with an impressive series of optimizations of the RCT's various mechanisms, to produce a very slow 15-glider recipe for a spacefiller... after which we might want to get back to the problem of finding ways to simulate the synthesis more effectively.

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #39, 25 June 2023: wickstretchers, more new oscillators, and greyship components

Matthias's message on the NewLifeCA discussion thread didn't so much contain "smaller items" in the sense of being less important, just in terms of pattern size. It seemed reasonable to turn the post into a full separate NewLifeCA message.

Many thanks, Matthias! I spent most of yesterday moving to a new apartment, so I very likely wouldn't have gotten all of this sorted out and summarized so nicely, at least not any time soon.

Wickstretchers
Expanding on the wickstretcher results from NewLifeCA #36, Keith Amling has found a c/5 diagonal barberpole stretcher, shown here with a new c/5 diagonal eater:

Code: Select all

#N c/5 diagonal barberpole stretcher and eater
#O Keith Amling, 8 April 2023
#C https://conwaylife.com/forums/viewtopic.php?p=160239#p160239
#C https://conwaylife.com/forums/viewtopic.php?p=160267#p160267
x = 77, y = 91, rule = B3/S23
22b3o$22b3o$25bo$20bo2bo$19b2o4bobo$15b3o4bo$15b3ob4o4bobo$14bobo2bobo
b2o$13bobo3bobo7bobo$12bo2b2obo2bobo$12bo2bo6b2o7bobo$13bobo5bo$19bo
13bobo$13bo6bobo$12b3o8b3o9bobo$11bob2o7bobobo$9b2o11b2o13bobo$8bo2bo$
8b3o13b3o12bobo$8b2o11bo$18b5o4b2o12bobo$8bob2o5b3o4bo$6bo4bo4bo4bo21b
obo$5b2o4bo4bobob2o$6b2ob2o6b2obo3bobo18bobo$6bo3bo8bobob2obo$5b2o3bo
12bo23bobo$4bobo3bo$3b2obob2o11bo27bobo$2bo2bo20bo$bo2bo17b7o22bobo$bo
2bo21b3o$2obo18b3o28bobo$o2bo2bo16bo32b2o$b2ob2obo15bobo28bob2o$2b2obo
2bo16b2o19bob2ob5o$2b3o2b3o35b2o2bo$2bo2b2o2bo11b3obo3b2o21bo$bo2bo4bo
11b2o4b4o13b2o3bo2bo$2bo5bo12b2o4bo16b3o2b3ob3o$2o4b3o19bo19bobo$o2b3o
38b2o4bobob2o$4b2o22b2ob2o14b2o3bo$5b2o23b2obo13bo2bob2o2bo$4b3o23b2o
2bo15b2o$3b2obo22bo4bo17bo3b3o$2bo3b2o21bo5bo22b2o$b2o2bobo23bo3bo15b
3o5b2o$bobo2b3o22b3obo15b2obo3b2obo$2b3obob2o20bo23bo5bo$3bo3b4o19bo
20b2o$5bobob3o34bobo2b3o$28bob3o12b2obo7b3o$5b2o20bobob2o12bo3bo5bo2bo
$26b2obo18b2o5bo2b3o$7b2o20bo13b3o2b2o6bo2b2obo$7bob2o31b2o4b2o9bobo$
6bo3bo17bo2bo9bo6b2o7b2obo$6b2o20bo12bo2b5o8b3ob2o$29bobo10b6o8bo2bob
2o$28bo15b2o9bo8b2o$5b2ob2o17b3ob3o22b3o3b3o$5b2ob2o17bo7bo19b2o5b3o$
4bo3bo17bob3o2bobo18b2o7b3o$4b4o21b3ob2o18bo2bo9bo$6b2o17b2o2bo2bo19bo
2bo11b3o2b2o$8bo20b2obobo16bo14bo5bo$27b2obo3bo10b3o2b2obo12b3o3bo$27b
2o2bobo10bo3b3obo15bobo$26bo2bo2bo11bo2bob2o20bo$26bobob2o11bobob4o18b
2obo$25bo16bobobo2b3o$30bo10bo5bo24b2o$24bo4bo11bob4o25bobo$24bo16bob
3o$23bo2bo48b2o$22bo52b2o$16bo3b2o$15b4o54b2o$14bo7bo50b2o$13b5o55b2o$
13bobobo52b3o$12b5o4bo42b2o4b3o$11bo5bo2bo43b2ob2o$10b2obo2bo47b3obo$
13bo2bo47bo4bo$14bo46b3o2bo2bo$61b2o3bo2bo$60bob4o$60bo7bo$61bo5bo!

Inspired by the wickstretcher discussion, Frank Everdij looked at some of his past c/6 diagonal spaceship results and found one that could stretch a tub. This is the first known c/6 diagonal wickstretcher of any type:

Code: Select all

#N c/6 diagonal tubstretcher
#O Frank Everdij, 10 April 2023
#C Using a ship found by Everdij, 10 March 2023
#C https://conwaylife.com/forums/viewtopic.php?p=142378#p142378
#C https://conwaylife.com/forums/viewtopic.php?p=160290#p160290
x = 87, y = 87, rule = B3/S23
15bo$13bo2bo$13bo3bo$12bo4bo$13b2obo$8bo7bo$7b3obob3o$6bo2b2obo2bo$5b
2o5b2o4b2o$6b2o9bo2bo$7bo9bo2bo$6bo10bo3b2o$3bo3b2o8bo2b4o$b2obobobo
11bob2o$4bobo10b2o6bo$o5b2o8bo8b2o$bo2b2o9bob5o3bo$2b2o5b4obobo4b3obo$
8bo5bobo5b4o2bo$8bo7bo11b3o$9b2ob2o2bo11bo$11b2o3b2o10b2o$11b3o3b2o9bo
$12b2o3b2o9b2o$18bo9b3o$14b5o11bo2bo$15bo14bo$32b2o$18b7o7b2o$19bobob
2o7bo$19bo4b3o4bo2b2o$30bo2b3o$27b3o5bo$25bob2o2bo3b2ob2o6bo$30b2o4bo
3bobo3b2o$30b4o2bo2bobobo2b2o$33b3ob2o4bo3bo$36bo4b3o$33bo2bo$33bobo8b
o$34bo8b3o$35bobo5bo2bo$34bo2bo5b2o4b2o$35b3o2b3obo2b2obo$39b2ob2ob7o$
40bo3bo2bo3bo$33b3o5bo2bo3b2ob2o$34b3o6b3o3bob2o$43b2obo2bob2o$42bobob
3ob2obo$42b3o4bobob2o$44b7o2b2o$46b3o4bo$49b4o$50b2o3b3o$54bob4o$54b2o
7bo$54b2o7bo$55bo2b2o3b3o$55bo2bo5b2obo$64bo2bo$69b2o$66bob3o$56b3o11b
o$58b3o$58b2o$62bo6b3obo$59b2o8b2obobo$62bo7bo$61b2o3b2o3bo7b3o$61b3o
2b3o2bob2o3bo4bo$66bo2b2obobo9bo$67bo3bo4bobo$66bo3bo3b3o2bo3bobo$67bo
2b2obobobo2b2o2b3o$73b2obo3b2o2b3o$72b2obo8b2o$74bo3bo$70bobo4bobo$69b
o3bo4bo$69bo4b2o$69bo4b2o2$70bo2bo$71bo2b3o$73b4o$74b2o!

Finally, Matthias Merzenich completed a 2c/5 orthogonal wickstretcher project using a partial result by Keith Amling and a wick that had been found by Merzenich in 2013. The discovery required heavy use of the spaceship search programs LLSSS, ikpx2, JLS, WLS, and knight2. This is the first known 2c/5 orthogonal wickstretcher of any type:

Code: Select all

#N 2c/5 orthogonal wickstretcher
#O Matthias Merzenich and Keith Amling, 23 April 2023
#C With reductions by Merzenich and Amling, 27-28 April 2023
#C https://conwaylife.com/forums/viewtopic.php?p=160785#p160785
#C https://conwaylife.com/forums/viewtopic.php?p=160944#p160944
#C https://conwaylife.com/forums/viewtopic.php?p=160947#p160947
x = 120, y = 295, rule = B3/S23
50b3o$50bo2bo$52b2o$50bo$50b6o$50bo5b2o$50bo4b3o$57bo$54b3o$51b4obo$
53b2ob2o$55bobo$54b4o$53b2o$53bobo2$52bo2bo$52b2o$54bo$52b2obo$52bobo$
55b2o$55bo$55bo$53b2o$53b2o$52bobo$52b2o$53b2o$52bo2$51b4o$50bobo2bo$
49b2obo$48bo2bo$53bo$51bo4bo$52bo3bo$53bo$49bob2o4bo$54b2ob2o$55bo2b2o
$57b3o$56bobo$57b2o$54bo2b2o$52bo2bobo$50b2obo2b2o$49bo3b2o2bo$49b2ob
2o2b3o$52b2o2b2o$41bo12b4o$40bobo12b2o$39b2ob2o$39bo2b2o14bo$38bobo14b
ob2o$38bobo11b2obo$36bo3bob2o9bobob2o$35bo4bo2bo8bo2b4o$35bo4b3o13b2o$
35bobo3bo2bo8bo2b2o$41b2obo12bo$41bo12b2ob2o$39b3o12b2obo$38bob2o11bob
ob2o$36b2o3bo11bobo2bo$36b2o3bo9bo3bo2bo$39bob4o5bo4bo$38b2obob2o5bo4b
3o$37b2obob2o6bobo3bo$37b2obobo14bo$40bobo13b2o$37b2obobo13b2o$37b2ob
2o13bo$38bo3b2o11b3o$39bo15b2o3b3o$63bo$40bo2bo10bobobo4b2o$40bo2bo10b
ob3obo2b2o$40bob2o18b2o$39b2obobo16bobo$39bo13b3o5bobo$38b4obo10bob2o$
39bo2bo11b4o$40bo13bo$56b2o$41b2o11bobob2o$41bo15bob2o$39b2o14bo5bo$
39b3o16b4o$40bob2o12bo6bo$41bobo15bo$43bo15bob2o$44bo14bo4bo$43bobo12b
ob2o2bo$42bo15b3o$41bo15bo5bo$40bo3b2o11b4o2bo$41bob3o9bo3bo$36b3o2b2o
12bobo3bo$36bobo3b2o13bo$36bobob4o10bobo$37bob2obo13bo$36bobob2o14b3o$
36bob2o$38bo18b2o$36bobo16bo$36b3o17b2ob2o$38b3o18b2o$39b2o15bo$55bo2b
o15bo$37b5o12bo2b2o14bobo$36bo2bo3bo10bobobo13b2ob2o$35bo4bo2bo9b2obo
15bo2b2o$36b2o18bo14bobo$40b2o14b2o13bobo$53b2obob3o8bo3bob2o$39b2o15b
obobo7bo4bo2bo$38b2o15b2obo2bo6bo4b3o$39b2o15bobob2o6bobo3bo2bo22bo$
36b2ob2o14b2obo3bo11b2obo16bo4b3o$55bo2bobobo11bo18b3o5bo$38bobo15bo3b
obo9b2ob2o15bo2b2o3b2o$35b3o2bo19bo5bo8b2o14bo5bo2b2o$35b3o2bo14b4obo
4bobo4b2obo15b2o4b2ob2o$37bo16bo2b2o5b2ob2ob2ob3o15b2o6b2o$35b3o19b4o
4bobobo29bo$41b3o13bob2o4bobobobo23b2o$34bo3bo2b3o9bo3bob2o4bob2ob2o
23b3o$34bo5bo2bo10bobob3o5bo29bo$34bo3b2o15bo9b3o$36bo3b2o22bo3b2o28bo
$36b2o17bob2o5bo2bob2o27bo$36bo18bo3bo5b2o2b2o25bo2bo$39b3o13bo4bo7b2o
29bo$36bo2b2obo14bobo4b5o28bob2o$36bo5b2o11bobo6b4o33b2o$37b2o17bo8b2o
31b2ob2o$38b2ob2o17b2o37bobo$37bo3bo16bobob2o34b2ob2o$37b3o17bo41bo$
38b2o18bob3obo32bo5bo$37b2o23bob2o30b2obo4bo$41b2o16bo2bo3bo17b3ob3o6b
ob2o3bo$37b2o2b2o16bo5bo18bobob3o6b2ob3o$41bo16bob2obo5bo13bo3b2o2bo4b
o2b2o$39b2o27b3o13b4ob3o3bo$39bo2bo14bobob2o5bo2bo10b3ob6o3bo3b2o$33b
3o21bobob2o6b2obo8b3o4bo6bo$33bo2bo20bobo3bo5b2obo2b3o4bo12bo2bo$29bo
4b2obo2b2o7b3o6b2o3bo8b4o2b3obo13b3o$23bo4bobo4bobo2bob2o5bobo7bo3bo4b
7o3bo2bo$21b2ob2ob2ob2o5bo2bobo2bo2bo2bo4bo5b2o2b5o6bo21b2o14bo$21b2ob
obobobo3bo2bo5b3o2bob2o5b2o3bo2bo3bo29b3o7bo4bobo$19bobo2bo4bo3b2o10bo
4bo7b4o3bo33bo8b3o2b2ob2o$18bob2ob2obobo5b2o2b2o3bo8b2o8bo3bo44bo3b3o$
17b2o5bo3b2obobobo4bob2o2b2obo3bo8b3o42b5obo2b3o$18bo4bo3bo2b2o23bo5bo
b2o41b2o5bo$18bo5b2o4b2o19bobo2b2o5bo41bobo4b2o$12b3o2bo8b2o24b2obo2bo
3bo43bo6b3o$12bobo2b2ob2obo27bo2b3o5b2o5bo45bo$12bo4bo3bo5bo7bo5bo5bo
13bobo3b2ob2o3bo35bobo$13b2o3b3o3bo2bo6b3o3b3o3bob2obo3bob2o2bo5b2o5bo
bo33bob2o$12bobo3b2o2b3o8bo2bo3bobo2b2ob2o6bobo4bo2bo6b2ob2o9bo7bo15b
2o$11b3o7b3o8b3o10bo2bo4b2obo4bo4bobo7b2o2bo5bobo4b2ob2o13bo$11b2o4bo
6bo8bobo4bo4b2o2b3o2bo4bobob2obobo4b7ob2o2b2ob2o3b2o9b3o6bo$b3o6bo4b2o
bobo3bo10b2o3bo14bo2b2o5bo2b3o5b2o3b2o2b2o2bo14bobo5bobo$bobo6b2ob3o3b
3obo7bo4bo13b2o4bobo3b3o3bob3o2b2o9b2ob2ob2obo7bo2bo5bo2bo$bo3bo3b2o4b
3obobo14bo12b3o5b2obob2o2b2o3bo3bo4b4obo3b2o3bo2bo4bob3o$bo4b2ob2obo7b
o10b2o3bo10bobo10bo8bo6bo3bob2o5b3o2bob2o4bobob2o5b4o$2bo5bo3b4o2b3o
12bo2bo6bo3b2ob2o5bo2bobo6bob3o7b2obo4b6o3b3obobob2o8bo$2b4ob4o3b2o3b
2o14bo5b2ob2o3b2o7bobobo5bo4bo4bo2bo7bo3bob2ob3obobo$8bo3bo3bo2bo2b2o
20b2o3b2o5bob3o3bo4bo10b2o2b2o5b2ob2o6bob2o9bo$3o6b2o3bo2bo4bo22bo10bo
4b2obo6bo15bo3bo3bob3o2bo10b2ob2o$b2o6bob3o2bo2bo20bo2b2ob2ob2o6b2o3b
2o5bob4ob2o11bo5bo2bobobobobo5bob2obo$6b2obo2bobo2b2o21b2ob2obob2o7b2o
bob2o7bo2bobob2o12bo3bobobo2bobo5b2o3bobo$7bob3o2bo5bo21bobo4bo10bo9bo
bo5b2o10bobo2b3o2bo2b2obo4b3o4b2o$4b2obo10bob2o21bo2b2o10bobo2bo4b2o2b
o4bo13bo3bo4b2o4bo6bo4b2o$3b2obobob2obo2b3ob2o20bob3o11bobobo5bo4bo4b
2obo8b5o5b2o2b2ob2o2bo2bo$4b5obo4b3ob2o23bo11bo3b3obo4b3ob2o2bo12bo7b
4o11b2o$5b3o6bo2bobo22bo4b3o6bob2o4bo8b2o3b4o8bo3bo3bob2o7bo3b2o$5bobo
3bo2bo27b3ob4o7b2o3b2o4bo7bo6bo8bobobo15bo$5bo5bo2b2o27bob2o3bo6b2obob
2o3bo8bob7o6b3o5b3o10bo$b3o9bobobo24b3o3bob2o8bo7bo2bo2bobo7bo4b2ob2o
5b3o7bo3b2o$3b2ob2o2bobo29bo3bo10bo2bobo5bob4o3b3ob3o5b3o19bo$4b2o4bob
o5bo22bo2bo4bo8bobobo19bobo7bo4b2o12bo2b2o$3bo11b3o22b2o3bob2o7bob3o3b
o15b3ob2o5b2ob2o2bo13bobo$4b2o8bo29b2o10bo4b2obo7b2o3b6o9bo2b2ob2o13b
2o$5bo8bo2bobo22b2obo11b2o3b2o8b2o2b4obo11b3o2b2o$18b3o21b3o12b2obob2o
9bob2ob2o2b2o$5bo9bo4bo21b3o15bo12bob2o5bobo9bo2b2o$4b2o9b3o25bob3o10b
obo2bo8b2o4b2o5bo3b3o2bob4o$4b2o8b2o2b2o23b2o2bo10bobobo15b2o4bo4bobo
4b2o2bo$3bo3bo5b3o3b3o15bo4bo13bo3b3obo9bo4bo3b2o4bobo8bob2o$3bo3bo4bo
5bo2bo14b3o2b3o2bobo7bob2o4bo9bo3bobo9b3o4b2o5bo$11bob2o4bo15bo6bo3bob
o8b2o3b2o9b2o3bo4bo6b3o4b2ob2o3bo$6bo4bo3b2ob3o14bobo4bo3bobo8b2obob2o
9b2o4bo3bo6bo5bobo7bo$2b2obo5b5ob2o18bobo3bo16bo13b2o8bo10b2obob2ob2ob
o$b2obo6bo4bo18bo4b5o3bo8bo2bobo8b2obo5b2obo9b2obobob3obob2o$5b2o8b2o
18bobo3b2ob3ob3o7bobobo7b2ob2o4bo13bo2bobo5b2o$6bo6bobo24bo9bo5bob3o3b
o5bobo5bob2o10bo12bo$4bo2b2o4bo2bo23bobo3b2obo6bo4b2obo6b2obo3bo2bo11b
2ob5obo$4bob3o7bo26bo13b2o3b2o7bo2bo2bo2bo14bobo3b3o3bo$3bobobobo5bo
24bo2b2o12b2obob2o14bobo10b3o5b3o2bo2bo$2b3o2b3o6bo3b3o13bo7b2o14bo10b
o6bo2bo9b3o5bo2bobobo$3b2o2b3o8bo3bo11b2ob2o3bobobo11bobo2bo11bo3b4o
10bo6b3o$5bobo10bo4bo10b2o6bobob5o7bobobo9bo2b3o3b2o10bobo4b3o$14b3o3b
o2b2o8bo6bo5bob3o5bo3b3obo8bo2b2o16b3o3b2o$14b2o5bo11bobo4b2obo7bo4bob
2o4bo10bo4bo12b2ob2o2b2o$14bo18bo7bo7b2obo4b2o3b2o5bo2b3obo18bob2o3b5o
$17b2o4b2o7b2o3b4o5b6o5b2obob2o4b3ob4o16bo4bo2b3o2b2o$13b2o8bo22bo5bo
7bo6bo5b3o16bobo3b2obo2bo3b3o$11bob3o6bo10bo2bo12b2o6bo2bobo7bob2o2b2o
14bo3b2o4b2o4b3o$10bo2bo6bobo10bo2bo2bo3b7o8bobobo6bo7b2o17b2o4bo5bo2b
o$9bo2bo7bobo10bo6bo2b2o2bo8bob3o3bo4bo3bo3b3o15bobo9b2o2bo$10bo3bo17b
5o19bo4b2obo7bo4b3o15bobo2b2o5b2o$11bobo18b3o2bo4bo5b2o7b2o3b2o8bo4b3o
15bo4bo6bo2bo$11bob3o17bobobo5bo5bo7b2obob2o6bo3bo19bo2bo2b2o7bo$10b2o
2b2o18b3o8bo4bo9bo10bob2o2bo15b5o3bo7bo$8bob4o20bo2bo9b2o9bobo2bo8bo3b
2o17bo3bo9b3o$7b2o3bo3bo16b2o2bo12b2o6bobobo13bobo17b4o6bo5bo$8bobo3bo
16b2obo2bo12bobo3bo3b3obo11bobo16bo2b2o2b2obobobo$7bo22bo6bo12bobo3bob
2o4bo9bo20b2o4bobo4bo$6bo24bo4b2obo7b3o7b2o3b2o8bob5o16b2o4b4ob3obo$6b
o3bo4bo17bo2b2ob2o16b2obob2o7b2o3bob2o14bo2bo4bob3o3bo$6bo7bobo17bo25b
o12b3o3b2o13bo6bo3bo3bobo$7bobo3b2ob2o20b2o6bob2o7bo2bobo10bo4b3o13bo
5bo6bo$7bo6bob2o17bo4bo4b2o11bobobo9bo2bo2b2o14bobobo4bo3bo2bo$9b2o3b
3o18bobo3bo14bob3o3bo3b3ob2o3bob2o15bo7bo4b2o$8b3o4b2o18bobo10bo7bo4b
2obo3bo2b7o16b4o7b2o2bob2o$13b2o17b3o3b2o6b3o8b2o3b2o4bobo8bobo16bo8bo
bo$12b3o29b2obo9b2obob2o4bobo4bo5bo12b2o7b3obob2o$30b2ob3o6b2obo2b2o
10bo8b3ob2o7bo13b2o8b2obo$14bo15bo2b4o8b2o2bo8bobo2bo7bob4obo2bo15b4o
2b2o4bob2o$13b3o14b2o3b2o4bo3b2o11bobobo4b2o2bobo26bo6bobob2o$12b2ob2o
13bo2bo7b2ob7o5bo3b3obo2b2o4bobo20bo2bo4bo2bobo$11bo2bo19b3o10b4o5bob
2o4bo8b2obo2b3o17bo4bo2b2obo$11bob2o14bo18b2o7b2o3b2o7b2o3bo2b3o14b4o
4b3o3bo$13b2o13b2o5b2o20b2obob2o10bo4bo2bo16b3o2bobo$11bo48bo8b3obobo
3bo14b2o3b3ob2obo$10b2obobo17bo2bo20bo2bobo5bo3b3o5bo13b2o3b3o2bo3bobo
$8b2obo3b2o15b3obo21bobobo8b2ob2o3bobo17b3o8bo$7bo4b5o14b4obo19bob3o3b
o11b2o21bo5bo4bo$7bobo2b3ob2o12b2o24bo4b2obo7bobo25bo3bobo$15bo14b2o4b
2o19b2o3b2o5bob5o2bo20b3o$8bo27b2o19b2obob2o6bo3b2o2bo22b3ob2o$8bo20bo
2bo4b2o21bo37bo4bo$31bo4bobo19bobo2bo12bo2b2o17bobobob3o$25bo32bobobo
15b2obo15bo2bobobo$24bobo3bobo4b2o17bo3b3obo11bo3b2o17bo2bobob2o$23b2o
b2ob2ob2o22bob2o4bo14bo17b3o4b2o2bo$23bo2bo3bo2bo23b2o3b2o16bobo18bo3b
o2b2o$21b2ob2o5b2ob2o21b2obob2o10b2o4bo20bo3b3o$22b2o9b2o25bo13bo3bob
2o21bob2o$23b2o7b2o23bo2bobo10bo2b2ob2o23bo$24bo7bo25bobobo17b2o19b2o$
21b2o11b2o5b2o8b2o3bob3o3bo16bob3o15b3o3b3o$22b3o7b3o7bo7bobo3bo4b2obo
19b2o15b2o3bob2o$25bobobobo6bobo5b2o2bo6b2o3bob2o16bo3bo15b2ob2o3bo$
37bob3o4bobob2o5b2obobobobo19bo16b2o5bo$35b3o5bo3b2o3bo6b2obobob3o12bo
20bobo$34bo3b4obo5b4o7bob3o4bo6bo3bob3o17b2o4b2o$35b2obobo3bo2b2o4bo3b
2obobobob2o2bo4b3ob2o20bo3b2o$36bobo2b2ob3o2b5o3b2obob2obo2b2o5bo4bo
20bobob2o$36bobo3bobo2b2o4bo6bobo2bo2bo9b2o21b3o$37b2obobo2bobo12bobo
3bobo5b2o22b2o$39bobobobobobo8bobobobo3b2o4b3o19b2ob2o$39bobob2o3b2o6b
3obobo3bobo5b2o20b2obobo$40bo14bo3bo5b2obo8b3o17bobo2bo$56bo2bobo2bo3b
2o10bo15bo6bo$57bobo2b2ob3o8bo5bo15bobobo$58bob2o5bo8bo5b2o12bo3bo$59b
o3bo3bobo7bo2bobobo11b2o2bo$60b2obo4b2o7bob2obobo9b3o2b2o$58bobo3bo13b
2obo2bo14bo$57bobo2b3o13b2o2b3o8bo4bo$57bo2b2o3bo13bo2bob2o7bo$58b2o2b
2o18bo2bo8b2o2bobo$60bobo19b4o15bo$60bo2bo18b2o14bo2bo$58b2obob2o15bo
18bob2o$59bobobo16bo16bo5bo$57bo2bobo33b2ob3o2bo$57b2obobobo31b2obo2bo
b2o$60bobo2bo31b3o4b2o$60bo4bo31b2obo$58bob4obob2o28b2o$57bobo4bobobo
31bo$57bo2bob2o2bo29bobob2o$58bobobobobo28b2o3bob2o$59bo2bob2o29b5o4bo
$60b2obo30b2ob3o2bobo$63bo32bo$63b2o38bo$103bo!

Small Oscillators
The records for smallest p26, p38, and p68 oscillators were broken over a span of 3 days:

Code: Select all

#N New smallest known oscillators of periods 26, 38, and 68
#C 60-cell p26 by Mitchell Riley, 19 April 2023
#C 42-cell p38 by Nico Brown, 21 April 2023
#C 38-cell p68 by Mitchell Riley, 21 April 2023
#C https://conwaylife.com/forums/viewtopic.php?p=160630#p160630
#C https://conwaylife.com/wiki/42P38
#C https://conwaylife.com/forums/viewtopic.php?p=160719#p160719
x = 102, y = 25, rule = B3/S23
52bo$51bo2bo36b2o$51bo2bo2bo33b2o$23bo29bo3bo$21b3o33bo31b4o$20bo68bo
2bo$7b2o11b2o$2o5b2o30bo$bo37b3o$bobo21bo16bo14bo22bo$2b2o19b2o16b2o
14b2o21b3o12bo$7bo11bo5b2o29b2o25bo12bo$7b2o9bobo3bo57b2o9bo2bo$2bo3bo
bo9b2o27b2o44b3o$2o5bo11bo26b2o14b2o$2b2o19b2o22bo14bo$bo21bobo37b3o$
25bo39bo15b2o$18b2o5b2o53bobo$5b2o11b2o60bo$6bo40bo31b2o$3b3o41bo3bo
46b2o$3bo43bo2bo2bo44bo$50bo2bo45b3o$52bo48bo!

Perhaps less glamorous, but still notable, forum user Period1GliderGun noticed that the p4 mold could interact with the p3 fire-spitting to give a nontrivial 31-cell p12 oscillator, breaking the 33-cell record held by dinner table for over 50 years:

Code: Select all

#N Mold on fire-spitting
#O Period1GliderGun, 18 May 2023
#C https://conwaylife.com/forums/viewtopic.php?p=161675#p161675
x = 15, y = 8, rule = B3/S23
5b2o$5bobo2bobo$b2o6bo2bo$o2bo3bo5bo$obo2bo3b3obo$bo12bo$2b2obo5b3o$4b
o6bo!

Other Oscillator Engines
Nico Brown discovered a p67 B-heptomino hassler, and while not the smallest (it's smallest phase is 8 cells or 3.5% bigger than the snark loop), it is the first engine-based p67 oscillator:

Code: Select all

#N p67 B-heptomino hassler
#O Nico Brown, 21 April 2023
#C https://conwaylife.com/forums/viewtopic.php?p=160728#p160728
x = 44, y = 44, rule = B3/S23
20b2o$10b2o3b2o2bobo$10b2o3bo3bo4bo$16b3ob5o$10b4o4bobo$10bo2bo4bobob
3o$19b2obo2bo$24b2o2bo$28b3o$31bo$12bobo15b2o6b2ob2o$26b2o11bob2o$9b2o
3bo11b2o5bo5bo$8bobo27b2o$8bo6bo2b2o11bobo$7b2o7b3o10bo11b2o$11b2o4bo
10bo11bobo$11b2o14b2o11bo$6b2o20b2o8b3o$2b2obobo21bo7bo3b2o$3bobo31b4o
2bo$3bob2o33bob2o$2obo33b2obo$o2b4o31bobo$b2o3bo7bo21bobob2o$3b3o8b2o
20b2o$3bo11b2o14b2o$bobo11bo10bo4b2o$b2o11bo10b3o7b2o$10bobo11b2o2bo6b
o$4b2o27bobo$4bo5bo5b2o11bo3b2o$b2obo11b2o$b2ob2o6b2o15bobo$12bo$13b3o
$15bo2b2o$18bo2bob2o$19b3obobo4bo2bo$23bobo4b4o$19b5ob3o$19bo4bo3bo3b
2o$22bobo2b2o3b2o$22b2o!

Brown also discovered a new p49 pi-heptomino hassler, and while not the first engine-based p49 oscillator, it can be used to construct the first engine-based p49 gun. This represents a significant improvement over previous p49 guns which required large glider loops.

Code: Select all

#N Engine-based p49 gun
#O Nico Brown, 18 April 2023
#C https://conwaylife.com/forums/viewtopic.php?p=160604#p160604
x = 96, y = 26, rule = B3/S23
17b2o$17bo$9bob2ob2obo43b2o$9b2obobobo6bo37bo$15bo6bob2o18bo8bob2ob2ob
o27bo$23b6o15b3o6b2obobobo6bo21b3o$26b3o7b2o9bo11bo6bob2o22bo$18b2o16b
2o8b2o19b6o18bo$4bo8bo3b2obobo47b3o7b2o9bo2bo$3bo3bo4bobo5b3o39b2o16b
2o13bo$7bo3bo3b4o4bo33bo3b2obobo25bo2bo$3b2ob2o4bo5b5o6b2ob2o3b2o13bo
3bobo5b3o26b2o$13b2o3b2ob2o6b5o5bo3bo6b2ob3o3b4o4bo$28bo4b4o3b3ob2o6bo
3bo5b5o6b2ob2o3b2o$b2o26b3o5bobo3bo13b2o3b2ob2o6b5o5bo4b2ob2o$o2bo25bo
bob2o3bo33bo4b4o3bo3bo$o13b2o16b2o39b3o5bobo4bo3bo$bo2bo9b2o7b3o47bobo
b2o3bo8bo$4bo18b6o29b2o16b2o$3bo22b2obo6bo21b2o7b3o$4b3o21bo6bobobob2o
24b6o$6bo27bob2ob2obo27b2obo6bo$34bo37bo6bobobob2o$33b2o20bo22bob2ob2o
bo$56bo21bo$54b3o20b2o!

Finally, Brown also found a new p53 oscillator. While not the first, nor the smallest, p53 oscillators are rare enough that it seemed worth mentioning.

Code: Select all

#N p53 pi-heptomino hassler
#O Nico Brown, 25 June 2023
#C https://conwaylife.com/forums/viewtopic.php?p=162952#p162952
x = 52, y = 25, rule = B3/S23
30b2o$17b2o3bo8bo$17b2o3b3o6bob2ob2obo$25bo6bobobob2o$24b2o7bo3$5b2o
24b2o$6bo25b2o11b2o$6bobo22b2o11bobo$2o5b2o35b2o$bo46b2o$bobo44bobo$2b
2o46bo$6b2o35b2o5b2o$5bobo11b2o22bobo$5b2o11b2o25bo$19b2o24b2o3$18bo7b
2o$12b2obobobo6bo$12bob2ob2obo6b3o3b2o$20bo8bo3b2o$20b2o!

Elegant c/5 Greyship Component Connections
Keith Amling has found some long sought-after connections between a c/5 greyship wick component and a more standard c/5 greyship component. Surprisingly, these new connections are extremely simple, requiring only a spider for support:

Code: Select all

#N Wick-based c/5 greyship connections
#O Keith Amling, 8-9 May 2023
#C https://conwaylife.com/forums/viewtopic.php?p=161321#p161321
x = 138, y = 86, rule = B3/S23
138o2$138o2$138o2$138o2$138o2$138o2$138o2$138o2$138o2$138o2$138o2$138o
2$138o2$138o2$138o2$138o2$138o$49bo$b4ob2ob2o2b4ob2ob2o2b4ob2ob2o2b4ob
2ob2obob2ob85o$o2b2o4b2obo2b2o4b2obo2b2o4b2obo2b2o4b2obob2obobo$2bo5bo
5bo5bo5bo5bo5bo5bo12b81o$57bo3bo$58b2o3b75o$46b5o5bo2bo3bo$49bobo4b3o
5b74o$45bo6bo5b2o$45bo3bo6bo3bo3b4o2b68o$46b2obo6bo13bo$49bob2o4bobo3b
2o6b67o$47b2o14b2o3bo3bo3bo$48bo15bo2bo4b4ob61o$46b2o17b2o4bo2bo3bo$
45bobo17bo5bo7b59o$45bob2o22bob2o$46bobo23bobo5b2o3b53o$48bo22b2o5bo2b
o3bo$78b2o6b52o$48bo31bo15bo$46bobo29b2ob2o3b2ob4ob2o3b3ob2ob2o2b4ob2o
b2o2b4ob2ob2o2b4o$45bob2o30b3o4bo2b2obo4bo2b2o4b2obo2b2o4b2obo2b2o4b2o
bo2b2o$45bobo32b2o3b2ob2o4b2o3bo5bo5bo5bo5bo5bo5bo$46b2o38bob2o$48bo
40bo$47b2o37b3o5b5o$49bob2o44bobo$46b2obo43bo6bo$45bo3bo43bo3bo$45bo6b
o41b2obo$49bobo45bob2o$46b5o44b2o$96bo$94b2o$93bobo$93bob2o$94bobo$96b
o2$96bo$94bobo$93bob2o$93bobo$94b2o$96bo$95b2o$97bob2o$90bo3b2obo$90bo
2bo3bo$93bo6bo$97bobo$94b5o!

Addendum:

Martin Grant has found a fencepost for an extremely simple period-8 wick that has been known since 1971:

Code: Select all

#N Fenceposts for an old p8 wick
#O Martin Grant, 16 June 2023
#C https://conwaylife.com/forums/viewtopic.php?p=162720#p162720
x = 84, y = 15, rule = B3/S23
9b2o6b2o3b2o36b2o3b2o6b2o$9bo8bo3bo38bo3bo8bo$10b3o5bobobo38bobobo5b3o
$2b2o3b3o3bo2b2ob2ob2o36b2ob2ob2o2bo3b3o3b2o$3bo2bo4b2obo2bo6bob2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o3bo6bo2bob2o4bo2bo$bo5b4o3b2o2b4ob3obo3bo3bo3b
o3bo3bo3bo3bo2b3ob4o2b2obob4o5bo$ob5o3bobo3b2o2bobobob2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b3obo3b2o3bo5b5obo$o6bo3b2ob2o2bobo42bobo2bob2o4bo2bo3b
o$b4obo6bo3b2obobo39b2obob2obo2bo3b2o3bo$4bobob5o5bob2obo2bo30bo2bob2o
7b7obobo$3b2o8b5o5b4o30b4o6b4o8b2o$4bob2ob2o2bo3b6o38b7o2bo2b2ob2obo$
2bobo2bobo4b2o6bobo34bobo6b2o4bobo2bobo$2b2o2bo2bo6b4o3b2o34b2o3b4o6bo
2bo2b2o$7b2o7bo2bo44bo2bo7b2o!

It can be hard to keep up with all of the interesting new oscillators being discovered these days. Fortunately, forum user Entity Valkyrie 2 has been reliably updating a stamp collection attempting to include every interesting oscillator with period above 13 found in 2023. They have also made stamp collections for 2021 and 2022 which give a sense of the rapid pace of oscillator discoveries in recent years.

Very few short, wide 2c/5 spaceships have been discovered so it was a surprise when new forum user Stanley Dodds found some new examples in May 2023:

Code: Select all

#N New short, wide 2c/5 ships
#O Stanley Dodds, 9 May 2023
#C https://conwaylife.com/forums/viewtopic.php?p=161340#p161340
x = 95, y = 39, rule = B3/S23
11bo3bo12b2o6bo3bo$10bobobobo9b2o2bo4b3ob3o$3bo5b2obo4bo5bo2b2obobo2bo
6bo6bo$2b2o5bo7bo3b2ob2ob3ob2o6b2obo4b3o$2obo3bo10bo5bo6b4o2b2o4bob4ob
2o$2bo2b2o13b3obo4bo12bo2bo5bo$5b2o2bo10bo2b3o4b2o$3bo13bobo4bo23b3o$
2obo20bo23b2o$23bo6$11bo3bo12bo7bo12bo3bo$10bobobobo9b2ob2o3b2ob2o9bob
obobo$3bo5b2obo4bo5bo2b2ob2o3b2ob2o2bo5bo4bob2o5bo$2b2o5bo7bo3b2ob2obo
3bobo3bob2ob2o3bo7bo5b2o$2obo3bo10bo5bo4bobobobo4bo5bo10bo3bob2o$2bo2b
2o13b3obo4bobobobo4bob3o13b2o2bo$5b2o2bo10bo2b3o13b3o2bo10bo2b2o$3bo
13bobo4bo15bo4bobo13bo$2obo20bo15bo20bob2o$23bo17bo6$11bo3bo8bo6b3o27b
3o6bo8bo3bo$10bobobobo5b2ob2o4b3o13bo13b3o4b2ob2o5bobobobo$3bo5b2obo4b
o4b2o6bo3bo11bobo11bo3bo6b2o4bo4bob2o5bo$2b2o5bo7bo2bo8bo2b3o10bo3bo
10b3o2bo8bo2bo7bo5b2o$2obo3bo8b8o2bo3bo5bo7b2obob2o7bo5bo3bo2b8o8bo3bo
b2o$2bo2b2o17b2o2b2o3b5o3b5o3b5o3b5o3b2o2b2o17b2o2bo$5b2o2bo3bo3b3o2b
2o3bob3o9bo2b2o3b2o2bo9b3obo3b2o2b3o3bo3bo2b2o$3bo15bo2bo3bo3b2o4bo3bo
13bo3bo4b2o3bo3bo2bo15bo$2obo12b2o9b2o7bo3bo13bo3bo7b2o9b2o12bob2o!

Hartmut Holzwart noticed that the widest of these actually supports a short 2c/5 wave and provided an additional waveguide of his own:

Code: Select all

#N 2c/5 waveguides
#C Left by Stanley Dodds, 9 May 2023
#C Right by Hartmut Holzwart, 8 June 2023
#C https://conwaylife.com/forums/viewtopic.php?p=162469#p162469
x = 147, y = 11, rule = B3/S23
11bo3bo8bo6b3o$10bobobobo5b2ob2o4b3o13bo21bo21bo21bo9bo$3bo5b2obo4bo4b
2o6bo3bo11bobo19bobo19bobo19bobo7bob2o4b3ob3o$2b2o5bo7bo2bo8bo2b3o10bo
3bo17bo3bo17bo3bo17bo3bo5b2ob2o3bobob2o2bo$2obo3bo8b8o2bo3bo5bo7b2obob
2o7bo7b2obob2o7bo7b2obob2o7bo7b2obobob3o6bo2b6o7b3o$2bo2b2o17b2o2b2o3b
5o3b5o3b5o3b3o3b5o3b5o3b3o3b5o3b5o3b3o3b5o3bobobo3bo2b2ob2o5bobo2bo3bo
$5b2o2bo3bo3b3o2b2o3bob3o9bo2b2o3b2o2bo9bo2b2o3b2o2bo9bo2b2o3b2o2bo9bo
2b2o2b2obo6bobo10b4o4b2o$3bo15bo2bo3bo3b2o4bo3bo13bo2bobo2bo13bo2bobo
2bo13bo2bobo2bo7b2obob3o3b2o12bo4b2o$2obo12b2o9b2o7bo3bo13bo2bobo2bo
13bo2bobo2bo13bo2bobo2bo8bo4bo19bo3b2o$116b3o23bo$143bo!

Short, wide ships have been essential to many greyship constructions so these new 2c/5 ships may help with the discovery of the ever-elusive 2c/5 against-the-grain greyship.

Keith Amling continues to demonstrate the power of his spaceship search program, LLSSS, with several new discoveries. First, waveguides at speeds c/5 diagonally and c/5 orthogonally:

Code: Select all

#N c/5 diagonal and c/5 orthogonal waveguides
#C c/5 diagonal left waveguide by Keith Amling, 7 April 2023
#C c/5 diagonal wave and right waveguide by praosylen, 25 April 2020
#C c/5 orthogonal wave and waveguides by Keith Amling, 7-14 June 2023
#C https://conwaylife.com/forums/viewtopic.php?p=160209#p160199
#C https://conwaylife.com/forums/viewtopic.php?p=162637#p162637
x = 304, y = 156, rule = B3/S23
124bo162bo$123bo2bo159bo2b2o2b2o$122bo3bo148bo7b4o3bo2b2o$122bo151bobo
5b2obo9bo$122bo2b2ob3o143bobo4bob2o3b3o$125bo3bobo143b2o3bobo5b3o$131b
o142bobobobobobo$127bo144bo2bo2bo5bo5bobo$127b2o142bo4bob2o3b3o4bo2bo$
125b3o4bo138bo3bo3bo$124b2o3bobo137b2ob2o16b2obo$124bo2bo140b4o11b2o7b
o2bo$125b2o2bo137b4o11b2obo9b2o$121b3o5bo136bo14bo3bo$120bo2bo141b2o
15bobo11bo$119b2o2bo139b2o2bo28b2o$122bo139bo19b3o11b2o$117bo144bo17b
3o14bo$116b2o141b2o2b2o14bob2o14bo$115bo143bo19bobo13b2ob2o$115bob4o
138b2o18bo19bo$116b3o136b2o2b2o17bo2bo13bo4b2o$112b2o141bo21b3o2bo15bo
$111bob2o137bo3bo20bo$111bo2bo136bo4bo18b3o2b3o14b2ob2o$111b2o138bo3bo
$109b4o136b2ob2o17bo3bo25bo$108b4o136b4o19bo29b3o$106b2o2b2o135b4o20bo
3bo$106b5o135bo20bobo4b3o$245b2o19b2ob3o26b3o$103b2o138b2o2bo20b4ob2o
23b2obo$103b2o137bo29b2o25b3o$102bo3bo135bo29bo2bo19b3o2bo$102bo3bo
132b2o2b2o29bo21b2o3bobo$103bo135bo34b3o19b2o5bo$99b3o2bo134b2o55b3obo
2bo$98bo2bo133b2o2b2o30bobo23bo$97b2o2bo133bo34b2obo2bo20b4o$100bo131b
o3bo34bob2obo21bobo$95bo135bo4bo32bo$94b2o135bo3bo32bo3bo28bo$93bo135b
2ob2o33b2o3bo27b2o$93bob4o129b4o67b2o$94b3o130b4o35b2o32bo$90b2o134bo$
89bob2o132b2o41b2o25bo3b2obo$89bo2bo130b2o2bo42b2o22bobob5o$89b2o131bo
76b2o$87b4o131bo46bobo22b2ob2o$86b4o129b2o2b2o45b2o$84b2o2b2o129bo52bo
23b3o$84b5o130b2o51bo$215b2o2b2o52bo21b3o$81b2o132bo60bo17bob2o$81b2o
129bo3bo57b2obo16bobo$80bo3bo126bo4bo57b2obo$80bo3bo126bo3bo55b3o$81bo
127b2ob2o54b2o$77b3o2bo125b4o55bobo$76bo2bo127b4o56bo2b2obo$75b2o2bo
126bo59b2o$78bo126b2o59b2o4b2o$73bo129b2o2bo60bo5bo$72b2o128bo65b2o2b
2o$71bo130bo65bobo$71bob4o122b2o2b2o62bo3bo$72b3o124bo72bo$68b2o129b2o
67bo3bo$67bob2o124b2o2b2o68b2o$67bo2bo124bo$67b2o123bo3bo76b3o$65b4o
122bo4bo74b2ob2o$64b4o123bo3bo78bo$62b2o2b2o121b2ob2o77b2o2bo$62b5o
121b4o84bo$187b4o77b3o2b2obo$59b2o125bo81b3o4bo$59b2o124b2o81bo$58bo3b
o120b2o2bo$58bo3bo119bo85b3o$59bo122bo84bo2b2o$55b3o2bo118b2o2b2o82bo
4bo$54bo2bo121bo91bobo$52b2o2b2o121b2o87bo2bobo$175b2o2b2o86bo4bo2bo$
54bo120bo92bob2o$50bo2bo119bobo94b2ob3o$49bob2o2b2o114bo3bo97b2o$48b2o
bo2b3o113bo$48bo2b5o113bo4b2o93b2o$50bo3bo115bobo95b2o2bo$46bo6bo111b
3o2b2o96bo3bo$46bo2b2o113bo2b2obo101bo$45bo2bo3bo112b2o4bo102bo$40b3o
2b3o120bo104bo$39bo7bo$38bo3b5o123b4o$38bo2bo3b5o118bo6bo$37b2obo6bo
120bo6bo$37bo2bo6b3o115bo2bo2b2o2bo2bo$38bobo123b2o12b2o$60b2obo3b4o
97b3o2b3o$38bo10b3o7bo2b3ob2ob5o94bob4obo$36bo4bo16bo3b2o2b2obo2bobo
92b2ob4ob2o$35b4obo8bobo6bo105b2o3bob2obo3b2o$35bo14bo7bo3bo5bo3bo91bo
bo10bobo$50bo3b2o7bo4bo97bo10bo$34bobo14b2o2bo4b2o10b2o2b2o86b3o10b3o$
34bo3bo13bo2b2obo4b2o6b2ob2o2bo2bo82bobo10bobo$36bobo19bo4bobo10b5obo
81bobo10bobo$29b3o4b3o31bo4b2o5bo81b2o12b2o$29bo2b2o36bobobo91bo2bo4bo
2bo$31b4o4bo31bo94b5o2b5o$28b2o4b2ob2o127b2o2bo2bo2b2o$5b2o26bo2b4o
127b4o2b4o$5b2o25bo6bo127bobo4bobo$4bo2bo24bo133b3obo2bob3o$2b2obo3bo
26bo126b2o14b2o$2b2obo3bo22b2ob2o126b2o3bo2b2o2bo3b2o$bo4bo3b2o19bo5bo
126bo3bo2b2o2bo3bo$3o4b2ob2o18bo2bo2bo128b3o2bo2bo2b3o$bobo3b2obo20bob
o2bo129bo10bo$b4o5bobo18b2o3bo130bo2bo2bo2bo$2bo2bo4bob3o15b4ob2o128bo
b2o2b2o2b2obo$5b2o7b2o12b2o4bob3o126bo3bo4bo3bo$11b2obo16bo2b2obo2bo
126bobo4bobo$11b2o2bo14bo7bobo128b2o2b2o$12bo18bo6bobo127bobo2bobo$11b
o3bo14bo137bo2b2o2bo$11b4o3b2o11bo5b2o129bobo2bobo$11bobo2b3obo15bobo
129b2o4b2o$12b2o2b2obo16bobo127bobo6bobo$12b2o21bo2bo126bo12bo$13bo21b
obo126bo3bo6bo3bo$15bo21bob2o123b2o12b2o$14bo19b4o129b2o6b2o$15bobo17b
ob2o2bo122b2obo8bob2o$17bo4b2o12bo3bo128b6o$17bobob2o12bob3o125bob10ob
o$21bo14bob2o131b2o$19b2o18b2o128bob2obo$168bo2b2o2bo$20bo15b2ob2o127b
o6bo$20bo2b2o8b2ob2o131bo4bo$19bo5bo7bo2bo$19bo15bo$20bob2obo10bo$24b
2o12bo$24b3o11bo$37bobo$24bobo4b2o4b2o$24bo6b2ob2ob3o$25bo2bo2b2o5b2o$
26bo2bo3bo5bo$27b2o!

At lower periods solutions can get even more absurd. Problems that would previously require unthinkably large solutions are suddenly being solved, as in these p3 supports capable of pushing a pi-heptomino at period-6:

Code: Select all

#N period-6 c/3 pi-heptomino pusher
#O Keith Amling, 19 April 2023
#C https://conwaylife.com/forums/viewtopic.php?p=160646#p160646
x = 107, y = 58, rule = B3/S23
14bo23bo29bo23bo$10b3ob3o19b2obo27bob2o19b3ob3o$9bo6b2o16bo4bob2o21b2o
bo4bo16b2o6bo$10bo3bo3bo4b3o7b2o6b2o21b2o6b2o7b3o4bo3bo3bo$5bo3b4o8b2o
bobo4b2obo3b2obobo19bobob2o3bob2o4bobob2o8b4o3bo$b3ob4o4b2o3b3o3bobo2b
2obo3bo5b2o19b2o5bo3bob2o2bobo3b3o3b2o4b4ob3o$o6b2o5bobob2obobob2obo5b
ob6o2bo17bo2b6obo5bob2obobob2obobo5b2o6bo$b2o3bo17bobo2b3o4bo3b2o23b2o
3bo4b3o2bobo17bo3b2o$18bob2o2bo3bo4b2obob6o19b6obob2o4bo3bo2b2obo$13bo
3b2obo6bo2b5obo33bob5o2bo6bob2o3bo$12b2o3b2obob2obo5bo4bobo5bo17bo5bob
o4bo5bob2obob2o3b2o$17bo3b3ob2ob2o3b2obobo6bo15bo6bobob2o3b2ob2ob3o3bo
$15bobo6bob2o5b4obo6bo15bo6bob4o5b2obo6bobo$13b2o8bo6bo7bobo2bo19bo2bo
bo7bo6bo8b2o$13bo2b2o5bob2obob3o5bob2o3bo15bo3b2obo5b3obob2obo5b2o2bo$
38bob2o2bo17bo2b2obo$23b2o10b2o5b3o17b3o5b2o10b2o$37b2o29b2o$37b2o5b2o
15b2o5b2o$24b2ob3o7b4obo4bo4b3o4bo4bob4o7b3ob2o$24b2o3bob3obo4b5o2bo3b
o3bo3bo2b5o4bob3obo3b2o$24b4obo5bo7bob2obo2b2ob2o2bob2obo7bo5bob4o$26b
2obo4b2o3bo8b2o7b2o8bo3b2o4bob2o$29bo3b2obobo3bo2bob3o7b3obo2bo3bobob
2o3bo$23b3o2b2ob6o2b2obo5bo9bo5bob2o2b6ob2o2b3o$25bo12b2o3bo2b2o11b2o
2bo3b2o12bo$25b3o2b2o2b2obo5bo2bo13bo2bo5bob2o2b2o2b3o$22b2ob2ob3o4bob
3obo4b2o11b2o4bob3obo4b3ob2ob2o$20bob2o4b2o3bo7bo3b3o11b3o3bo7bo3b2o4b
2obo$19b2o3bobo3b2obo4bo29bo4bob2o3bobo3b2o$16bo2b2o2bob2ob2obobob6obo
b3o13b3obob6obobob2ob2obo2b2o2bo$15bobobo2bo10bob5o3bo19bo3b5obo10bo2b
obobo$14bo5bo2b2o7bobo5bo4bo15bo4bo5bobo7b2o2bo5bo$14bo10bo6bob2obo2bo
3bo17bo3bo2bob2obo6bo10bo$18bo2bo3bo7bo2b3o2bo2bo17bo2bo2b3o2bo7bo3bo
2bo$14b2ob2o2b2o9b4o3b2obobo17bobob2o3b4o9b2o2b2ob2o$13bobobobo11b2o2b
obo2bobob2o15b2obobo2bobo2b2o11bobobobo$13bo5bo8b3o3bo5bobob2o15b2obob
o5bo3b3o8bo5bo$14bo3b3o3b3o5bobo2b2obobo21bobob2o2bobo5b3o3b3o3bo$19b
2o2bobobob4ob2ob4obo21bob4ob2ob4obobobo2b2o$23bobobobobobobobob3o23b3o
bobobobobobobobo$24bo2bo2b2o9b2o21b2o9b2o2bo2bo$25bobobo5bo2bo29bo2bo
5bobobo$15b2ob3ob2o5bobo2bo37bo2bobo5b2ob3ob2o$15b2o4bo6b2obo43bob2o6b
o4b2o$14bo2bob2o7bo6b4obo25bob4o6bo7b2obo2bo$29bo8b4o23b4o8bo$37bo4bo
21bo4bo2$37b2o29b2o$35b3ob2o25b2ob3o$32b2o4b4ob2o17b2ob4o4b2o$32b2o4b
2o3b2o17b2o3b2o4b2o$31bo5bo3b4o17b4o3bo5bo$34b2o5b2o21b2o5b2o$34bo7bo
21bo7bo$35bo6bo21bo6bo$34bo37bo!

For an even more impressive result, you may wish to gawk at this c/4 diagonal multi-tubeater found by Amling on 23 June 2023. It sets the record for steepest descent of a multi-tubeater for tubs at the minimal spacing. Can you spot the unnecessary non-interacting glider?

[dvgrn]

NewLifeCA #40, 14 July 2023: A p19 appears, and (not related) POTY 2022 voting is underway at last

Period 19 Found -- Only Period 41 Remains!
Mitchell Riley has turned up a period-19 pre-honeyfarm hassler, in a new corner of the ever-larger search space for medium-period oscillators.  The search space expands each time a new catalyst is found, or a new active reaction is investigated, or a new configuration of catalysts becomes available to search engines.

It turned out to be a fairly simple structure:

Code: Select all

#N Cribbage
#O Mitchell Riley, 14 July 2023
#C Found with Riley's 'symmetric CatForce' search program
#C https://conwaylife.com/wiki/Cribbage
x = 32, y = 21, rule = B3/S23
4b2o$4bo$b2obo10bo$bo2b2o9b3o$3bo2bo11bo$bob3obo9b2o$obo4bo$o2b3o15bo
$b2o2bo5bo8b2o7b2o$3b2o6bo16bobo$3bo7bo8bo7bo$bobo16bo6b2o$b2o7b2o8bo
5bo2b2o$10bo15b3o2bo$24bo4bobo$13b2o9bob3obo$13bo11bo2bo$14b3o9b2o2bo
$16bo10bob2o$27bo$26b2o!

-- Simple as these things go, anyway.  Recent searches for new dependent reflectors have been turning up lots of new oscillators lately, all quite a bit larger than this new p19, with a wide variety of periods from the mid-twenties to the mid-nineties.

However, nothing much with a period lower than twenty has showed up in these dependent-reflector searches so far.  This led some people (such as me) to make the incautious prediction that a period 41 oscillator was more likely than a p19 to be discovered next.

Goldtiger997 has worked out a complete 69-glider synthesis of the 'cribbage' p19 oscillator already:

Code: Select all

#N 69-glider cribbage synthesis
#O Goldtiger997, 14 July 2023
x = 204, y = 227, rule = B3/S23
195bo$193b2o$194b2o3$7bo$8b2o180bo9bo$7b2o181bobo7bobo$190b2o8b2o$3bo$
bobo$2b2o17bobo$16bobo3b2o$17b2o3bo176bo$bo15bo181bobo$2bo6bobo187b2o$
3o7b2o$10bo2$201bo$194bo4b2o$187bo5bo6b2o$18bo168bobo3b3o$19b2o16bo
149b2o$18b2o18b2o$37b2o146bo$33bo150bo$31bobo150b3o$32b2o3$30bobo$31b
2o$31bo5$33bobo$34b2o$34bo11$185bo$185bobo$185b2o9$170bobo$170b2o$171b
o2$148bo4bobo$147bo5b2o$147b3o4bo2$153bo$152bo$152b3o4$63bo$64b2o$42bo
20b2o$43b2o92bo$42b2o76bo15bo$58bo59b2o16b3o$59b2o58b2o$47bo10b2o$48b
2o79bo$47b2o79bo$125bo2b3o$62bo60b2o$60bobo61b2o$61b2o$74bo$75bo$73b3o
49bobo$125b2o$126bo2$86bo$84bobo$85b2o4$94bo$92b2o$93b2o3$71bobo$72b2o
$72bo11$83b2o$84b2o$83bo3$82b3o$84bo$83bo2$65b3o$67bo$66bo6$53b3o$55bo
$54bo6$122bo$121b2o$121bobo4$164b2o$164bobo$164bo3$75b3o$77bo$61b3o12b
o$63bo$62bo2$151b2o$150b2o$132b2o18bo$131b2o$133bo5b3o$40b2o97bo23bo$
39bobo98bo21b2o$41bo120bobo2$175b2o$174b2o$41bo134bo$41b2o$40bobo104b
3o$142b3o2bo$142bo5bo$143bo$181bo$40bo6bo132b2o$40b2o5b2o131bobo$39bob
o4bobo2$36b2o138bo20b3o$37b2o136b2o20bo$36bo138bobo20bo8$183b3o$183bo$
184bo$190b3o$190bo$191bo10$193bo$192b2o7b3o$192bobo6bo$202bo3$200b2o$
200bobo$200bo$12b2o$11bobo181b2o$13bo180b2o$196bo3$8b2o$9b2o$8bo!

Predictions on how long it will now take for a p41 to turn up are ... well, let's just say, they're many and varied.  If past experience is any guide, we might find several more p19s in quick succession, for absolutely no reason beyond some obscure corollary of Murphy's Law.

This is more or less what happened with period 23, as you'll see in the nominee list in the next section.

Pattern of the Year 2022
As often seems to happen, the process of gathering and researching and wordsmithing Pattern of the Year 2022 nominations turned out to be an unconscionably huge amount of work.  A new conwaylife.com forum user with the handle 'b3s23love' recently picked up the scattered pieces and got things back on track, with help as usual from Matthias Merzenich.

Now there's an actual voting thread, with voting in progress until the end of July.

There are still a couple of weeks left.  Please feel free to drop by and vote if you haven't already, or just to have a look through the list of nominees and see if you missed anything interesting last year.

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #41, 22 July 2023: Omniperiodic! Also, diesuperduperhards!

The NewLifeCA message count has reached a very auspicious number, mostly but not entirely by coincidence.

Omniperiodicity Arrives At Last!
Nico Brown's search program -- a hacked version of LocalForce that showed up less than a month ago, at the end of June -- has been generating dozens of dependent reflector loops of various periods over the past few weeks.  In some cases, many unrelated mechanisms have been turning up with the same period.  Period 66 has been wildly improbably popular, for example.

Yesterday the program finally produced a period-41 180-degree dependent reflector.  It seems inevitable with hindsight, but until it actually showed up, it seemed possible that everyone would keep throwing darts at the periodic-oscillator dartboard indefinitely and hitting every other period except for the bullseye "41".

As usual with these dependent reflectors, multiple copies can be trivially connected to produce the first ever period-41 oscillator, the final unknown period for Conway's Life:

Code: Select all

#N p41 dependent reflector loop
#O Nico Brown, 21 July 2023
#C https://conwaylife.com/wiki/204P41
x = 73, y = 61, rule = B3/S23
34bo$32b3o$31bo$16b2o13b2o$17bo$17bobo$18b2o$28bo$27bo$29bo$27b3o4$40b
o$5b2o24b2o5bobo$6bo24bo7b2o$4bo13b2o12b3o$2b4o15b2o11bo$bo14b2obo$o2b
3o10b2o3bob2o$b2o2bo10b2obo3b2o$3b2o16bob2o$3bo14b2o$4bo6b3o7b2o26bo$
b3o7bo38b2o$bo5b2o3bo11bo24b2o$8bo14bobo$5b3o15b2o$5bo2$67bo$48b2o15b
3o$47bobo14bo$22b2o24bo11bo3b2o5bo$21b2o38bo7b3o$23bo26b2o7b3o6bo$53b
2o14bo$48b2obo16b2o$48b2o3bob2o10bo2b2o$48b2obo3b2o10b3o2bo$53bob2o14b
o$38bo11b2o15b4o$38b3o12b2o13bo$32b2o7bo24bo$32bobo5b2o24b2o$32bo4$43b
3o$43bo$45bo$44bo$53b2o$53bobo$55bo$40b2o13b2o$41bo$38b3o$38bo!

Shortly after that came completions of previous known p41 partials, such as Achim Flammenkamp's p41 toroidally supported wick from the previous millennium.

Other associated discoveries that turned up very quickly included a series of true-period p41 guns, starting with large and complicated stream-supported designs, and working quickly down to more reasonable sizes such as the following:

Code: Select all

#N true-period p41 gun
#O iNoMed, 22 July 2023
#C https://conwaylife.com/forums/viewtopic.php?p=164030#p164030
x = 112, y = 90, rule = B3/S23
71bo$71b3o$74bo$73b2o13b2o$88bo$86bobo$86b2o$76bo$75bobo$74bo3bo$74bo
3bo$74bo3bo$55bo19bobo$55b3o18bo$58bo$41bo15b2o14b2o$41b3o19bobo8bo$
44bo18b2o6b3o17b2o$43b2o19bo6bo9b3o7bo$56bo23bo3bo4bobo$57b2o20bo5bo3b
2o$57b2o10b2o7bo3bo3bo$47b2o20b2o7bo2bobo2bo$46b2obo4bo23bo3bo3bo$47bo
b2o2b2o20b2o2bo5bo$48b2o4bo19bobo3bo3bo$74bo6b3o$73b2o$62b2o27bo$34bo
27bo27b2o$32b3o5b2o11b2o8b3o24bobo$31bo7bobo11bobo9bo16b2o$16b2o13b2o
6bo8bo6bo26b2o$17bo20b2o9bo5b2o$17bobo27b3o$18b2o$28bo$27bo$29bo$27b3o
70b3o$93b2o5bo9b2o$66b2o26bo6bo8bo$66b2o16bo9bobo11bobo$40bo16bobo24b
3o8b2o11b2o$5b2o24b2o5bobo17b2o27bo$6bo24bo7b2o17bo27b2o$4bo13b2o12b3o
40b2o$2b4o15b2o11bo31b3o6bo$bo14b2obo45bo3bo3bobo19bo4b2o$o2b3o10b2o3b
ob2o39bo5bo2b2o20b2o2b2obo$b2o2bo10b2obo3b2o38bo3bo3bo23bo4bob2o$3b2o
16bob2o38bo2bobo2bo7b2o20b2o$3bo14b2o43bo3bo3bo7b2o10b2o$4bo6b3o7b2o
26bo9b2o3bo5bo20b2o$b3o7bo38b2o6bobo4bo3bo23bo$bo5b2o3bo11bo24b2o7bo7b
3o9bo6bo19b2o$8bo14bobo31b2o17b3o6b2o18bo$5b3o15b2o50bo8bobo19b3o$5bo
69b2o14b2o15bo$91bo$73bo18b3o$48b2o22bobo19bo$47bobo21bo3bo$22b2o24bo
11bo10bo3bo$21b2o38bo9bo3bo$23bo26b2o7b3o10bobo$53b2o18bo$48b2obo$48b
2o3bob2o$48b2obo3b2o$53bob2o18b2o$38bo11b2o23bo$38b3o12b2o9bo11b3o$32b
2o7bo20bobo13bo$32bobo5b2o21b2o$32bo4$43b3o$43bo$45bo$44bo28bo$53b2o
19b2o$53bobo17b2o$55bo$40b2o13b2o$41bo$38b3o$38bo!

Glider syntheses have also appeared already for the original version of the dependent reflector loop, among other things.

There's a bit of cheerful scrambling going on now on the forums and Discord, trying to figure out what open problem the comunity might shift its collective attention to next.

Diesuperduperhards
The "diesuperhards"  (my invented placeholder term, it's terrible, don't use it), from mid-April of last year, were such a huge step up from regular diehards that it seemed hard to imagine needing to take any more steps.  Nonetheless, another step has now been taken -- or maybe several steps, depending on how you count them.

Last year's diesuperhards fit in a 10,000-cell bounding box, and took so long to die off completely that it wasn't possible to write the order of magnitude of the lifespan in a reasonable-sized email, let alone the actual lifespan.

Now these new diesuperduperhards -- also an awful term, sorry! -- have taken a further step from the ridiculous toward the sublimely ridiculous.  It's getting difficult to write the number of "121"s in the tower of exponents representing the lifespan.  These tetrational diehards die off completely after the very rough order of 121^121^121^ ... 121 ticks, where the number of "121"s in the expression is something in excess of 10^950, and still working its way upward.

And the patterns *still* fit in the same 10,000-cell bounding box!  Here's the latest version as of today:

Code: Select all

#N diesuperduperhard work in progress
#O toroidalet, 22 July 2023, building on work by several others
#C See the dedicated forum thread:
#C https://conwaylife.com/forums/viewtopic.php?p=164007#p164007
x = 109, y = 91, rule = B3/S23
18b8o20b12o4b5o2bo15b2o15bo$19bo4bo22bo3b2o8b2obob4obo13b2o8b2o5bo$41b
2o4bo4b2o9b4o27bo2bo4bo$42bo4b2o46b2o8b2o$42bobo8bo3bo24b2o21bobo$43b
2o3bob2obo2bo25b2o22bo$48b2o6b3o3b2o$37b3o8b2o12b2o21b2o8bo$28b2o6b3o
46b2o6b3o4b2o$28b2o13bo9b3o36bo7b2o$42bobo8bo38b2o$43bo8b3o$21b2o17bo
5bo4b2o7b2o35b2o7b3o$21b2o6bo9bobo3bobo4b2o6b2o4bo30b2o6bobo$29b2o7bob
o5bo2bobo13bobo37bo$29b2o6bobo3bo22b2o35bobob2o$30bo5bobo3bobo6bo2bo5b
2o20bo2bo19b2obo$35bobo5bo6bo2bobo3bo2bo21b4o9bo6bobobo$34bobo13bo3bob
o3b2o19bo13b2o9b2o$33bobo19bobo24b2o2b2o8b2o8bo$32bobo21bo45b2o$19b2o
3b2o5bobo6b2o5b2o4bo28b2o17bobo$19b2o3b2o4bobo7b2o5bo4bobo3b2o21b2o18b
o$20b5o6bo13bobo5bo4bobo21b2o4b2o10b2o$21bobo21b2o12b2o13b2o14bo$35b2o
37b2o11bo$21b3o4b2o5b2o51b2o$28b2o23b2o22b2o14bo8b3o$53bo23b2o13bo2bo$
42bo8bobo13b2o23bo2bo$40bobo8b2o14bobo13b2o9bo$19b2o4b2o5b2o4b2o28b2o
4b2o6bobo$20bo4bobo4b2o4b2o24bo9b2o6b2o5b2o$17b3o6b2o10b2o23bobo13bo9b
2o$17bo22bobo11b2o8bo6bo6bobo23bobo$29bo12bo10bobo14bobo4bobo12b2o11b
4o$28bobo22bo16bobo3bobo13b2o9bob2o$23b2o4bobo20b2o17bo5bo6bo18bo4bo$
25bo4bobo12b2o11b2o8bo5bo7b3o18b3ob2o$22bo8bo12bobo10bobo7bobo3bobo5bo
7b2o13b3obo$23b2o19b2o10bo2bobo6bo5bo6b2o6b2o12bo3b2o$41bo14b2o2b2o3bo
5bo33bobo$35b2o3bobo10bo10bobo3bobo12bo17bo2bobo$35b2o4bo10bobo10bo5bo
13bo18bobo$16bo36bo8bo5bo9b3o4bo$16b3o42bobo3bobo8b3o9bo$19bo42bo5bo8b
o3bo8bo$18b2o39bo5bo24bo$b2o8b2o9b2o27b2o5bobo3bobo9b2o3b2o$5o6b2o8bo
2bo8b2o16b2o6bo5bo$2ob2o16bobo3b2o3bobo5b2o14bo5bo$5b3o14bo3bobo3bo6bo
bo13bobo3bobo7bo$2o2bo3bo17b2o3b2o6b2o9bo5bo5bo7bobo$2bo2bo5bo3b2ob2o
16bo13b3o6bo11b2o23b2o$9b4o2bo3bo15bobo6bo8bo4bobo34bo2bo$b4o3bob3o3b
3o17bo6bobo6b2o5bo36bobo$bo5bo4b2o29b2o11bo32b2o6bo$4b3ob2o21bo5bo9b2o
6bobo23b2o6b2o$2o3bo2bo2bo4b3o3b2o6bobo3bobo8b2o7bo3bo15bo4bo$ob3o3b2o
b2o2bo3bobobo5bobo5bo22bobo12bobo4b3o$2o2b2ob2o2b2o2b2ob2ob2o5bobo24bo
4b2o14bo7bo7b2o$o2b3o5bo17bo16bo9bo35b2o9bo2bobo$2o3bo2b2o3bo12bo11bo
6bobo6b3o47bobobo$o5b4o15bobo10b2o6bo15bo4b2o10b2o8b2o14bo$2obo5bobo
14bo11b2o3b3o15bo2bo2b2o11bo8b2o17bo$o3bob2o3bo27bo3bo17bo2bo15bobo23b
o$bo7b2o19b2o31bo17b2o21b2o2bo$b3ob2o8bo13bobo18bo3b4obo10bo32b3ob2o$
3bo4bo5bo2bo4b2o4bo2bobo15bobo5b2o6bo4b3o30b2o3bo$b2o2bo3bob2obo2bo4bo
bo3b2o2b2o3bo5b2o4bo2bo3bo2bo4bobo6bo30b2ob2o$obo2b3o4bo5bo4bobo10bobo
3bo7b2o4bobo2bo2b2o6b2o30bo$2ob3obo5b5o6b2o11bo7bo9bo47b3o2bo$2ob2o2bo
bo4bobobo15bo8b2o10b2o3b2o41b2obobo$14b5o14bobo21bob2obo$15bo7bo10bo
13b3o2b2obo10bo$16b4o30bo2b3o2bob2obo2bobob2o$17bo3b2o7bo17b2o7bo3b2o
2bob3ob2o24bobobobo2bo$23bo5bobo20bo2b4obo5b6o27bob2o2b2o$24bo2bo2bo
21bob2o14bo31b2o2bobo$25bo21b2o2b2o3bobobo36bo2bobo5bo$25bo20bo7bo43b
3o2b3o2bo$40bo2bo2bob3o5bobo41b3o4bo$26bo17bo4b2ob5ob3o38b4o4b2o$26bob
2obo8b3o4bobo2bo3bo4bo6bo19b2o7b5o3bob2o$25b2obobob2o8bo2bobobo5bo5bo
5b2obo17b2o8bobobo5bo$26bob3o10b3obo4b3ob2o3bobo5bo34b2o$27b2obo3bo5b
2o5bo3b3obobo2bob2o3b3o3b2o10b2o5b2o7bobob3o$28b3ob2o6b2o2b2o2bo2bobo
3bo4b2o5bob5o9b2o5b2o6bob7o$30bo11b2obo7bo3bobo3b2o6bo3bo24b2ob2obo$
31b2o7b2obob2obobobobob2o2bob3o7b3o20b2o$32bo7b3o4b8o5bob2o8b3o20b2o!

-- I hope I've described this correctly.  However, probably if a correction has to be sent out, there will be another update needed soon in any case.

The short summary is that back in April 2022, diesuperhard lifespans were pushed up gradually from about the eighth tetration of 121, to somewhere above the twelfth tetration of 121.  After these recent sudden jumps, diesuperduperhard lifespans are now creeping up toward the 10^1000th tetration of 121.

Keep the cheer,

Dave

[dvgrn]

NewLifeCA #42, 27 August 2023: POTY, Continued Oscollecting, and Impressive New Grey Matter

Here's another NewLifeCA contribution from Matthias Merzenich -- thanks, Matthias! For the LifeViewer-enabled original, see here.

---beginquote---
2022 Pattern of the Year voting ends soon
Voting for the 2022 Pattern of the Year ends on 1 September 2023 at 00:00 UTC. If you wish to participate, the voting thread is linked here.

p93, p126, and New Oscillator Stamp Collections
New oscillators continue to roll in. Of note is a p93 R-pentomino hassler, the first engine-based p93. All previous p93 oscillators were formed from adjustable signal loops or an interaction between p3 and p31 sparks.

Code: Select all

#N p93 engine-based oscillator
#C completed by iNoMed on 1 August 2023
#C based on a partial result by Carson Cheng
#C https://conwaylife.com/forums/viewtopic.php?p=164406#p164406
x = 57, y = 61, rule = B3/S23
9bo4bo$7b2obo2bob2o$5bo12bo$5bo12bo$2o2bo14bo2b2o$2o3b2obo6bob2o3b2o$
5b3o2bo2bo2b3o6$5b3o2bo2bo2b3o$2o3b2obo6bob2o3b2o$2o2bo14bo2b2o$5bo12b
o9b2o$5bo12bo9bo$7b2obo2bob2o9bobo$9bo4bo11b2o3$22b2o$21bobo$21bo2bo$
22b2o$23bo10$33bo$33b2o$32bo2bo$33bobo$33b2o3$29b2o11bo4bo$28bobo9b2ob
o2bob2o$28bo9bo12bo$27b2o9bo12bo$33b2o2bo14bo2b2o$33b2o3b2obo6bob2o3b
2o$38b3o2bo2bo2b3o6$38b3o2bo2bo2b3o$33b2o3b2obo6bob2o3b2o$33b2o2bo14bo
2b2o$38bo12bo$38bo12bo$40b2obo2bob2o$42bo4bo!

Mitchell Riley found a new p126 R-pentomino hassler which, after reductions by iNoMed and Matthias Merzenich, is the smallest known oscillator of this period based on its minimum population of 52 cells:

Code: Select all

#N Smallest known p126 oscillator
#O Mitchell Riley, iNoMed, and Matthias Merzenich, 27 August 2023
#C https://conwaylife.com/forums/viewtopic.php?p=165849#p165849
x = 42, y = 20, rule = B3/S23
8bo$9b2o$7b2o$9bo5$21b2o$20bo2bo$19b2ob2o$21bo$2o36b2o$o2bob2o31bobo$b
3obobo32bo$5bobo32b2o$3b2obo10b2o$2bobobobo9bo$3bo3b2o6b3o$15bo!

Nico Brown noticed that it could be turned into a gun using an existing method which, after reduction by iNoMed, is the smallest known gun of this period based on its bounding box of 41x34=1394 cells:

Code: Select all

#N Smallest known p126 gun
#O Nico Brown and iNoMed, 27 August 2023
#C https://conwaylife.com/forums/viewtopic.php?p=165853#p165853
x = 41, y = 34, rule = B3/S23
27b2o$27bo2b2o$28b2ob3o$34bo$28b2ob3o$9bo18b2obo$7bobo$8bobo$8bo$17bo
16b2o$16b2o16b2o$15bo$16bo$21bo$21b2o$20b2o2$2o$o2bob2o32bo$b3obobo30b
obo$5bobo31b2o$3b2obo10b2o$2bobobobo9bo15b2o$3bo3b2o6b3o15bobo$15bo18b
o$37b2o$36bo2bo$34bo2bobo$33bo4bo$33bo$24bo10b3o$22b2o6bo$24b2o5bo$23b
o5b3o!

Most new oscillator discoveries aren't included in these newsletters. To get a more complete picture of this year's oscillator discoveries, see Entity Valkyrie's 2023 oscillator stamp collection. There are also stamp collections for 2021 and 2022.

Recently, David Raucci and Carson Cheng have been working on a comprehensive collection of oscillators by scraping the forums and old pattern collections. A download link for their enormous stamp collection is available here. Unfortunately, this collection doesn't include any metadata beyond the period, but it does show just about every interesting known oscillator (and a large number of uninteresting ones).

c/6 Diagonal Ship and Pushalong
Frank Everdij has found a new c/6 diagonal spaceship and an associate pushalong using Adam P. Goucher's ikpx2 search program:

Code: Select all

#N c/6 diagonal spaceship and pushalong
#O Frank Everdij, 1 August 2023
#C https://conwaylife.com/forums/viewtopic.php?p=164432#p164432
x = 222, y = 192, rule = B3/S23
11b2o$10bobo$10bo$10b2o$10bob3obo$10b2obo2bo$14bo3bo$15b2obo$16bob2o$
12bo3bo2bo$b5o6bo3bo3b2o$o2bobo6bobobobob2o$2o2bo4b3o3bo2bob2o$4b2o13b
o8b2o$4bobo4bo4bo2bo7b2obo$7bo4bo2b2o2b2o4b2o2bo$4b2ob5o2b3o2bo4bo2bo$
17b2o2bo5b2o$6b3o2b2o4bo4b2o3b2o3bo$8b2o3b4o10b2o2bobo$10b3o2bo8bo2b2o
b2obo$10b3o4bo10bo2bo$18bo7b2o$18bo$16bo3bo9b2ob2o$15bo11b2ob2o3bo$15b
o6bo4b2o4bob5o$14bob5obo2b2o7b2ob3o$13b2o2b5o3b2o11b3obo$13bobo21b2obo
$14bo5bo3b2o10b2ob2o$19b3o2b2o11bobobo2bo$18bo18bobo2b2o$19b2o3bobo13b
2o$24bo2bo8bo3b2o6bo$25b3o8bo9b3o$26bo3bo3b2o10bo3bo$26b2ob4o4b2ob2o2b
o3b3o$26b4o7bo2bob2o5bob2o$26b3ob3o8bo5bo3b2o$28b3o2b2o2b2o5b6ob2o$31b
ob2o2bobo3bo4bo$28bo3bo5bo8bo3bo$32bo5bo2bo6b4o7bo$31bo5bo2bo7bobo7bob
o$40bo7b2o7bo$35b2o3bo8bob2o2bobo$35bo3b2obo12bo$34b2obo2b2ob3o5b2ob2o
3bo$37b2obo2bob2o3bobo2b2ob2o$36b2o5b2o4bobobo2b3obo58b3o$38b3ob2o2bob
obo2bo6bo57bo$38b3o5bob2o3b3o2bobo56bo$50b3o5b2o57bo2bo5bo$48bo3bo9b2o
56b2o2b2obo$46b4o2bo6b2o2bo53b2ob2o2b2obo$49b2o10bo2b4o51bob2obo$45b2o
3bo7b2obob2o47b2obo9b3o$44bo4b2ob2o3bob3o5bo4bo38bo3bo4bobobob2o$43bo
4b2o3bobob2ob3o2b2ob4obo36bo5bo5bo3b2o3b3o$44bo5b3o2bo2b2o4b3ob3o39bo
2b3o2bo2b2o8b4o$56b4o2b4ob4o3bo35bo3b3o3bo4bo4bo3bo$54bo4bobo6b2ob2o3b
o39bob3o4bo5bobo3bo$54b2obo3bob2obobo4bo3bo57bo2bo$56b2o2b2obob2o11bo
35b3obo20bo$56bo2b3o2bobo6b2ob3o35b2obo3b2o12bobo2bo$56bo2b2o2b3o7bo
39bo3b3o15b2o4bo$56bobo2bo17b3o32b2ob3o14bob6o$59b5o15b3o52bo$59b4o17b
o54bo$59b3o20b2o37bo17b2obo$59bo2bo12b2o5b3o34b2obo16b2o2bo$58bo3bo11b
3o3b2o37b2o18b2o$59bo3bob2o11bo2bo37b2obo18b2o$61bo3bo6bo2bobo2b2o38b
2o5b2o$71b2obo2bo3bobo39bob2o2bo11b3o$62bo2bo5b2o9b2ob2o39b2o$63bobo8b
2o8b3o35bo2bobo11b3o2bo$64b2o7bo10bo2bo35bo3bo10bobo$67b2o16b3o36bo2bo
2b3o4bo2bo2bo$67b3o2bobo10b3ob3o33bobo2b3o4b4o3bo$67b2o3b4o12bo37b2o5b
obobo5b2ob2o2bo$70b2o4bo10bo42bo2bobo8bo3bobo$70b2o3b2o10bo2bo5bo34bo
3bo3bobo3bob2obo$71bo5b2o11b2o2b2obo39bo2b3o3b3o$76b2ob2o6b2ob2o2b2obo
45bo4b3o$76b2ob2o8bob2obo46bo2bo6bob4o$78b3ob2obo9b3o43bob2o3bo4bob2ob
o$81bo3bo4bobobob2o44b4obobo3bo4b2o$80bo5bo5bo3b2o3b3o41bo2bo2bo$80bo
2b3o2bo2b2o8b4o36b3obo11b2obo$80bo3b3o3bo4bo4bo3bo41bo2bo7b2o2bo$86bob
3o4bo5bobo3bo50bo3bo$105bo2bo37b3o15b2o$84b3obo20bo36bo13bobo3bo$84b2o
bo3b2o12bobo2bo35b2o11b2o2bo2bo3bo$83bo3b3o15b2o4bo34b2o13bo4bo2bo2bo$
84b2ob3o14bob6o38b2o7b2o5bobo3bo$104bo42b2ob3o10bo3bo4b2o$105bo42bo6bo
bo5bo4bob2obo$91bo17b2obo37bo3b2obo6bo3b2o4bo$89b2obo16b2o2bo37bo4bo6b
o3bo7bo$89b2o18b2o41bobo8bob2o8b2o$89b2obo18b2o42bo2b2ob2obo10b2o$90b
2o5b2o54bo6bo2bo7b6obo$93bob2o2bo11b3o39bo8bo8b3o5bo$96b2o56b4o4bo16bo
$92bo2bobo11b3o2bo43bo2bo12bo$93bo3bo10bobo46bob2o14bo$94bo2bo2b3o4bo
2bo2bo42bo3bo11b2ob3o$95bobo2b3o4b4o3bo40bo3bo11bo3bo2b2obo$96b2o5bobo
bo5b2ob2o2bo38bo4b2o4bobo4b3o2b2o$100bo2bobo8bo3bobo35b3o5b2o3bobo5bo$
101bo3bo3bobo3bob2obo37b2o4b2o3bo9bob3o$107bo2b3o3b3o41bo3bo2bo11bo$
113bo4b3o40b4o3b3o$111bo2bo6bob4o35b3o4bo10b3obo$111bob2o3bo4bob2obo
40bob2o7b3ob4o$112b4obobo3bo4b2o34bo5b2o14bobob2o$115bo2bo2bo43b2o3b2o
b2o5b2o8b2o$111b3obo11b2obo45b2obobo4bo$116bo2bo7b2o2bo38bo2bo2b2ob2o
6bo3b2o2b2o$128bo3bo38bobo2b2o10bo4bob2o$116b3o15b2o35bobo15bo5bo$116b
o13bobo3bo39b2o13b2obo$116b2o11b2o2bo2bo3bo36bo15bo4b3o$116b2o13bo4bo
2bo2bo34b2obo12bo4bobo$120b2o7b2o5bobo3bo34bo3bo10bobo3bob4o$117b2ob3o
10bo3bo4b2o34bo3bo15b3o$118bo6bobo5bo4bob2obo39bo15b2o2bo$120bo3b2obo
6bo3b2o4bo33b2o12b2obo2bo$121bo4bo6bo3bo7bo32b2obo2bo7b2o3b3o2b3o$122b
obo8bob2o8b2o34bo2bo2bo2b2o2bo7bob3o$125bo2b2ob2obo10b2o35bo2b2o3b2o3b
6obobob2o$123bo6bo2bo7b6obo35bo2bo4bo6b6obobo$123bo8bo8b3o5bo31b3o6bo
2bo2b3o6bo4bo$124b4o4bo16bo31b2o10bobo7bo3bo3b2o$128bo2bo12bo46bobobo
2bo3bo3bobob3o$127bob2o14bo39b4ob2obobobo5bobo5b2o$126bo3bo11b2ob3o37b
o2b2obob2o16bo$125bo3bo11bo3bo2b2obo33b5o3b2o12bo5b2o$129bo4b2o4bobo4b
3o2b2o33bo6bo12bo2b6o$126b3o5b2o3bobo5bo39bo3b4o2bo9bo7bo$128b2o4b2o3b
o9bob3o33bobobo2bobobo10bo2b3o$130bo3bo2bo11bo41b4o13b2o4b2o$131b4o3b
3o51bo2bo2bo15bo3b2o$132b3o4bo10b3obo37b3o2bo16b3obob2o$139bob2o7b3ob
4o35bo2bo3b3o14b2obo$134bo5b2o14bobob2o32bo2bo6bo14bo$135b2o3b2ob2o5b
2o8b2o41b2o$146b2obobo4bo38bobo3bo$140bo2bo2b2ob2o6bo3b2o2b2o29b4obo$
141bobo2b2o10bo4bob2o29b3o2bobo$141bobo15bo5bo34b2obo$146b2o13b2obo35b
2ob4o$147bo15bo4b3o30b2obobo$147b2obo12bo4bobo35bo$147bo3bo10bobo3bob
4o33bo$148bo3bo15b3o34b3o$153bo15b2o2bo31bo2bo$148b2o12b2obo2bo37b2o$
148b2obo2bo7b2o3b3o2b3o31bo$151bo2bo2bo2b2o2bo7bob3o$152bo2b2o3b2o3b6o
bobob2o$154bo2bo4bo6b6obobo$151b3o6bo2bo2b3o6bo4bo$151b2o10bobo7bo3bo
3b2o$161bobobo2bo3bo3bobob3o$155b4ob2obobobo5bobo5b2o$155bo2b2obob2o
16bo$155b5o3b2o12bo5b2o$157bo6bo12bo2b6o$157bo3b4o2bo9bo7bo$157bobobo
2bobobo10bo2b3o$161b4o13b2o4b2o$162bo2bo2bo15bo3b2o$162b3o2bo16b3obob
2o$163bo2bo3b3o14b2obo$164bo2bo6bo14bo$173b2o$165bobo3bo$166b4obo$166b
3o2bobo$170b2obo$170b2ob4o$171b2obobo$176bo$177bo$175b3o$175bo2bo$176b
2o$176bo!

Although the amount of c/6 diagonal technology has grown in the last three years, it's still relatively rare to find new spaceships at this speed.

Record-Breaking c/5 Greyship
Keith Amling continues to amaze with his complex greyship searches. Back in July he found a new c/5 orthogonal greyship with a much steeper descending component than was previously known:

Code: Select all

#N c/5 orthogonal greyship with a record-breaking descending component
#O Keith Amling, 21 July 2023
#C https://conwaylife.com/forums/viewtopic.php?p=163987#p163987
x = 450, y = 243, rule = B3/S23
255b2o$254bo$253b2o$253b2o3bo$253b2o2bo$255bo$251bo2b2o$212b3o35b2o2bo
$212b4o36bo2b2o$211b2obobo33bo$215bo$210bo2bo37b3obo$211bo2bo38b2obo$
211bo2b2o$212b3o33bo5b2o$211bobo33b2o2b2o2bo$211b3o33bo2b2obo$210bo$
210bo2bo34bobo$211bob2o32bo4b2o$212bo34bob2o2bo$247bo$212bo$211bob2o
30bo2bo80bo5bo$210bo2bo31b3o79b2o5bobo$210bo33bo79b2o3bo4b2o$211b3o29b
o80b2o2b2o$211bobo30b2o80b2obo5b3obo$212b3o108bo6b2o2bo2bo2bo$211bo2b
2o30b2o74bob2o5bo8bo$203bo7bo2bo31b3o19b2o37bo4b3o5bo4bo6b2obo$202bo2b
o4bo2bo32bobo18b3o36bobo3bo3bo2b2o12b2o$192bo22bo32b2o16b2o2bo26b5o12b
o4b2o13bo$191bo2bo6b2o3bo4b2obobo29bob2o19b2obo20bo3b2o3b2o2b2ob5o2b2o
4b2o$181bo19b5o6b4o27b3o2bo17b2o2bob2o18bobo13b6ob3o$180bo2bo6b2o3bo8b
o7b3o27b3o2bo19bobo2b2o5b2obo9bob6o4b2o10b2o$170bo19b5o5b6o35bobobobo
17b2o10b2o3bob3o2b2obo4b2obo3b2o$169bo2bo6b2o3bo8bo7bo3bo6bo27b2o3b3o
15b3o8b2o4b5o4b2ob2o7bobobo$159bo19b5o5b6o6bo3bo6bo32b2o15b5o13bo3b3o
3b2o9bo2bo$158bo2bo6b2o3bo8bo7bo3bo6bo10b3o47bo4bo8b2ob2o6bobo$148bo
19b5o5b6o6bo3bo5b2obo10b2o27b2o17b2o15bob2o4bo$147bo2bo6b2o3bo8bo7bo3b
o6bo9bo2bo10b2o23b2ob3o18bo2bo16bo4bobo$137bo19b5o5b6o6bo3bo5b2obo7b5o
11bo22bo2bo20bobo15b2o7bo$136bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o9b3o
23bo22bobo$126bo19b5o5b6o6bo3bo5b2obo7b5o8b2o10b2o16b3o5bob2o$125bo2bo
6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o19bobo25bobo19bo$115bo19b5o5b6o6bo3bo5b
2obo7b5o8b2o9b2o8bo20b2o5b2o6bo12bo2b3o37bo$114bo2bo6b2o3bo8bo7bo3bo6b
o9bo2bo8bob2o18bob2o6bo2bo15bo3bo5bo6bo8b3o3bobo22b2o14bobo$104bo19b5o
5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o7bob3o8b2o2bo4b3ob3o5b2o2bo5bobo2b3ob
2o6bo13b3o16b2ob3o$103bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2b
o10b3o8bo3b2o3b5ob2o4bo4b2o2b2o2bo12bobo14bo7bo5b2o5b2o$93bo19b5o5b6o
6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo21bobo2b2obo6b2o2b2ob2o2b3ob2ob2o11b
o4b2o4bob2ob2o6b3o6bo3bob2ob2o$92bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o
18bob2o6bo2bo8bo25bobo3bo2bobo3bo2bob2o3b2o5bo14bob4o7b3o14b2o3b2o$82b
o19b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo9b2o14bobo2b3o4bobob
o9b2o10b2o3bobo12b2o3b3o5b3o3bob2obo2bobo$81bo2bo6b2o3bo8bo7bo3bo6bo9b
o2bo8bob2o18bob2o6bo2bo8bo10bo3bo8bo2bo5bo2b3o5b2o3bo2bob2obo6bo13bo3b
2o3bo2b4ob2obob4ob2o4bob2o2b2ob2o5bo$71bo19b5o5b6o6bo3bo5b2obo7b5o8b2o
9b2o7b5o6b2obo8bo3bo5b6o8bo7bo4bo10bo7bo6bo14bobo5bo3bo2bobo3bo2b3o4bo
bo7bo4b2o3bo$70bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10b
o3bo9bo10bo2bo2b2obobo3bo7bobo13b3o19b2o6b2o6b2o4b2o16b2obo$60bo19b5o
5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo5b6o6b5o18bo3b2o8bobo16b2o
3b2o3b3o6bo7bo6bo$59bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo
8bo10bo3bo9bo7b2o3bo9bobo3bo32bo4bo5b4o$49bo19b5o5b6o6bo3bo5b2obo7b5o
8b2o9b2o7b5o6b2obo8bo3bo5b6o6b5o20b2o5b2o2bo28bo2bobo2bo$48bo2bo6b2o3b
o8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo6bo2bo10bo2b
6o19bo5bo6bo2bo$38bo19b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo
5b6o6b5o19bo12b2obo2bo19b2o5bobo9bo4b4o$37bo2bo6b2o3bo8bo7bo3bo6bo9bo
2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo6bo2bo17bo4bobobo17b2o3bo4b
2o11b2o3b3o6bo7bo6bo$27bo19b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8b
o3bo5b6o6b5o19bo11b2o5bobo2b2obo19b2o2b2o31b2o6b2o6b2o4b2o16b2obo$26bo
2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo6bo
2bo18bo11bo2bobobo19b2obo5b3obo13bobo5bo3bo2bobo3bo2b3o4bobo7bo4b2o3bo
$16bo19b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo5b6o6b5o19bo11b
2o6bo3bo5b2ob2o2b4o5bo3b2o5bo6b2o2bo2bo2bo12bo3b2o3bo2b4ob2obob4ob2o4b
ob2o2b2ob2o5bo$15bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo
10bo3bo9bo7b2o3bo6bo2bo18bo10bobo9b2o3bo7b2o2b2o4bob2o5bo8bo13b2o3bobo
12b2o3b3o5b3o3bob2obo2bobo$25b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo
8bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo9b3o10bo2b4o2bo4bo6b2obo23bob4o7b3o
14b2o3b2o$14b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b
2o3bo6bo2bo18bo10bobo7b4o5b3o14b3o4b2o12b2o21bo4b2o4bob2ob2o6b3o6bo3bo
b2ob2o$14b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo5b6o6b5o19bo
11b2o6bo3bo6bobo7bo4bo6bo10b3ob3o4b2o13bo22bobo14bo7bo5b2o5b2o$17bo7bo
3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b
4o6b3o2bo3bo11bo3bo2b2o7b2o34bo13b3o16b2ob3o$13b6o6bo3bo5b2obo7b5o8b2o
9b2o7b5o6b2obo8bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o5b3o8bo
65b2o14bobo$14bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo6bo
2bo18bo10bobo7b4o6b3o2bo18bobo4bo7b2ob3o70bo$14bo3bo5b2obo7b5o8b2o9b2o
7b5o6b2obo8bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o11b2o12b
3o$14bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b
4o6b3o2bo18b2o9bo2b2ob2o3bo2b3o3bobo9b2o$13b2obo7b5o8b2o9b2o7b5o6b2obo
8bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o10b4ob3o6bo7bo
8b4o30b2o$13bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo6bo2bo18bo10bo
bo7b4o6b3o2bo18b2o7bo6b2o4b2o2b2o4bobo4b3o2bo11b2o11bo16bo$13b5o8b2o9b
2o7b5o6b2obo8bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b
2o3bo5b3o5bob4o3bo7b6obo2bo2b2o2b3o2bobo15b2o$14bob2o18bob2o6bo2bo8bo
10bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o3bo5bo
2bo7bobo2b2ob2o2b2o2bob5o5bob2o2bo13b2o5bo$15b2o9b2o7b5o6b2obo8bo3bo5b
6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo4bo4b2o3bo
8b4o5b5obobo3b2ob2ob3o4bo9b2ob3o2b2o$25bob2o6bo2bo8bo10bo3bo9bo7b2o3bo
6bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo3b3o2bo6b2o7b3o3b
2o3bobo2bo3b3o5bo2bo5bo2b2obobo2bo6b2o$15b2o7b5o6b2obo8bo3bo5b6o6b5o
19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o3b3o2bo2bo4b
3o5bob2o10b3obo3bo4bo4bo4b2ob3o2bo6b4o$14bob2o6bo2bo8bo10bo3bo9bo7b2o
3bo6bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo12b2ob2o
6b3o14b2o2bobo2bo2b2ob4o5bob2o6b3ob2obo$13b5o6b2obo8bo3bo5b6o6b5o19bo
11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b16o2bo29b2o4bo
bo11b2ob2o2b6o8bobo$13bo2bo8bo10bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b4o6b
3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo18b2ob2o39b2o2b2obob2ob2ob4o12bo$
13b2obo8bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo
7b2obo6b6o4b27o32bobo4bo11bobobob2obo$14bo10bo3bo9bo7b2o3bo6bo2bo18bo
10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo30b2o3b4o23bo2b3o8b3o
b2o7bo$14bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo
7b2obo6b6o4b40o2b2o2b3o35bo3b4o5bo$14bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b
4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo43bo3bobo37bobo3b3o$13b6o6b5o
19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b52o4b2o2bo
37bo5bo$17bo7b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo
3bo4bo7bo56b3o5bo$14b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3b
o7b2obo6b6o4b65o2bob2obo$14b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo6b
2o3b3o2b3o5bo3bo4bo7bo68bo5bo$27bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b
2o9b2o3bo7b2obo6b6o4b77o5bob2obo$15bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo
6b2o3b3o2b3o5bo3bo4bo7bo81b2obob2obo$16bo11b2o6bo3bo6bobo7bo4bo5bo2b2o
7b2o9b2o9b2o3bo7b2obo6b6o4b91o4b3o$26bo10bobo7b4o6b3o2bo18b2o7bo6b2o3b
3o2b3o5bo3bo4bo7bo93bo122bo$17b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o
3bo7b2obo6b6o4b102o4b2o2b2o86b2o4bo19bo20b2o$15bo10bobo7b4o6b3o2bo18b
2o7bo6b2o3b3o2b3o5bo3bo4bo7bo106bo3bob3o72b2o11b2o5b2ob2o14bobo14bo2bo
2bo8b3o$14bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b116o79bo2b
o10b2obob4o2bo14b2obo5bo6bo2bob3o6bo$15bobo7b4o6b3o2bo18b2o7bo6b2o3b3o
2b3o5bo3bo4bo7bo122bo74b3o7bo5b2o2bo3b3o11bo4bo3b2obo6bo3bo7b2ob3o3b3o
$14bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b128o3bo3b2o74b2o2bo3bo
2bo2bo6bo9b3o3b3o6bobo3b2o2bo6bo2bo2bo3bo$14b4o6b3o2bo18b2o7bo6b2o3b3o
2b3o5bo3bo4bo7bo131b2o2b3o2bo67b4o3b2o4bob2o6b3o8b3o10bo3b4o6bo4b2ob2o
2bo3b2o$13bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b141ob3o4bo61bo9bo2b2o
4b2o3bo4b2o7b2o2bo7bobo4bo9b3o2b3o2b3o2b2o12bo$13b3o2bo18b2o7bo6b2o3b
3o2b3o5bo3bo4bo7bo144b2ob2o63bobo2bo2b2ob2o2bobo4bo2bo8bo4b2o10b2o3bo
4b2o5bo4bo4b3o2bobo10bobo4b2o7b3obo3b2o$13bo2b2o7b2o9b2o9b2o3bo7b2obo
6b6o4b153o67bo4bo3b2ob2o3bo7bo9b3obo12bo2b5o10bob3o4bo4b3o9b2o5bo2bo6b
2obo3b3o2b2o$26b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo156b2o3b4o60bo3b2o3b2o9b
3o9b2o2bo13b2o3b2o11bo3bo3bo19bobob2o5bo3bob2o6bo15bo5b3o$14b2o9b2o9b
2o3bo7b2obo6b6o4b166o2b2o2b3o53b2obo3b3o16b2o12bo18bo41b2obobo6b2o3b2o
2bo3b3o7b2o3b5o$15b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo169bo3bobo53b3obo4bo
90bo4b2ob2o4bo5bo2bo4b2o6bo8b6o2bo$14b2o9b2o3bo7b2obo6b6o4b178o4b2o2bo
51bo3bo93b3o8b2o9bo3b3o4bobobo5bo2bob2o4b2o$13bo6b2o3b3o2b3o5bo3bo4bo
7bo182b3o5bo48bobo2b5o88b2obo9bo10bo7b2o3b3o5b2o3b2o$14b2o3bo7b2obo6b
6o4b191o2bob2obo16b2o6b2o7bobo14bob4o86bo3bo2bobo27bobo2bo5b4o4bo$14b
3o2b3o5bo3bo4bo7bo194bo5bo3bo11b4o6bo5bo2b2o5b2o7bob2o3bob2o34b2o16b2o
16bo8b2obob2obo31bo7bobob2o$5b2o9b2obo6b6o4b203o5bo3b2o10b5o3bo2b2o4bo
3bo4b4o7bo7bo2bobob2o4bo17bo3bo2bo9b3o2b7o12b2ob2obobob4obo41bo4b3o$4b
o2bo8bo3bo4bo7bo207b2obob2o11b2o4b4o2bo4bo3bo5bo2b3o13b2o2bob3o2b2o6b
2o9b2o3bobo5bo6bo2bobobo3bob2o3bo5bo3b2o4b2o4bo38bo2bo3bo$5b3o7b6o4b
217o4b2o19bo2b2o4b2obob2o3b2o3bo2b2obo2bo5b5o4bob2obobob2o12bo9b3o4bo
6bo8b2obo3bo8bob3o43bo$4bo3bo5bo7bo219bo5b2o2bo2bob4o2bo2b3ob6o3b2ob2o
2bo3b2obo2b3o8bo7b3o6bo10bo4b2o4b2ob2o12bo3b6o3bobo3bob2ob2o2bobobo$4b
4obo4b228o7bob4o2b3o2b2o5bobo3b4ob2obo3b2ob2o2bobo19bo4b2ob2obob3o3bo
8b2o4bob3o6b2ob2obo6b7o8bobo2bo$3bo5bobo232bo5bo2bo4bo6bo2b2o6bo3b4o3b
3o4b3o14b2o3bo5bob2o5bo3b2o10bo13bo13b2o14bo$2b3ob2o3b234o3bobo2b3o8b
2o4bo3bo8bo3b3o22bo3bo5bo13bo3bo2bo2b3o$2bo3b3o236bo2bo2b2o2bo3bob2o3b
ob3o14bo25bo2bobo4b2ob4o2b2ob2obo4bobo6bo$b2o5b237o4bo6bo2bo3b4o2b2o9b
5o26b2ob3o5bo2bo7b4obobo3b7o$3o246b2o16b4o45bo5b2o3b3o9b3o$b2o5b237o4b
o6bo2bo3b4o2b2o9b5o26b2ob3o5bo2bo7b4obobo3b7o$2bo3b3o236bo2bo2b2o2bo3b
ob2o3bob3o14bo25bo2bobo4b2ob4o2b2ob2obo4bobo6bo$2b3ob2o3b234o3bobo2b3o
8b2o4bo3bo8bo3b3o22bo3bo5bo13bo3bo2bo2b3o$3bo5bobo232bo5bo2bo4bo6bo2b
2o6bo3b4o3b3o4b3o14b2o3bo5bob2o5bo3b2o10bo13bo13b2o14bo$4b4obo4b228o7b
ob4o2b3o2b2o5bobo3b4ob2obo3b2ob2o2bobo19bo4b2ob2obob3o3bo8b2o4bob3o6b
2ob2obo6b7o8bobo2bo$4bo3bo5bo7bo219bo5b2o2bo2bob4o2bo2b3ob6o3b2ob2o2bo
3b2obo2b3o8bo7b3o6bo10bo4b2o4b2ob2o12bo3b6o3bobo3bob2ob2o2bobobo$5b3o
7b6o4b217o4b2o19bo2b2o4b2obob2o3b2o3bo2b2obo2bo5b5o4bob2obobob2o12bo9b
3o4bo6bo8b2obo3bo8bob3o43bo$4bo2bo8bo3bo4bo7bo207b2obob2o11b2o4b4o2bo
4bo3bo5bo2b3o13b2o2bob3o2b2o6b2o9b2o3bobo5bo6bo2bobobo3bob2o3bo5bo3b2o
4b2o4bo38bo2bo3bo$5b2o9b2obo6b6o4b203o5bo3b2o10b5o3bo2b2o4bo3bo4b4o7bo
7bo2bobob2o4bo17bo3bo2bo9b3o2b7o12b2ob2obobob4obo41bo4b3o$14b3o2b3o5bo
3bo4bo7bo194bo5bo3bo11b4o6bo5bo2b2o5b2o7bob2o3bob2o34b2o16b2o16bo8b2ob
ob2obo31bo7bobob2o$14b2o3bo7b2obo6b6o4b191o2bob2obo16b2o6b2o7bobo14bob
4o86bo3bo2bobo27bobo2bo5b4o4bo$13bo6b2o3b3o2b3o5bo3bo4bo7bo182b3o5bo
48bobo2b5o88b2obo9bo10bo7b2o3b3o5b2o3b2o$14b2o9b2o3bo7b2obo6b6o4b178o
4b2o2bo51bo3bo93b3o8b2o9bo3b3o4bobobo5bo2bob2o4b2o$15b2o7bo6b2o3b3o2b
3o5bo3bo4bo7bo169bo3bobo53b3obo4bo90bo4b2ob2o4bo5bo2bo4b2o6bo8b6o2bo$
14b2o9b2o9b2o3bo7b2obo6b6o4b166o2b2o2b3o53b2obo3b3o16b2o12bo18bo41b2ob
obo6b2o3b2o2bo3b3o7b2o3b5o$26b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo156b2o3b4o
60bo3b2o3b2o9b3o9b2o2bo13b2o3b2o11bo3bo3bo19bobob2o5bo3bob2o6bo15bo5b
3o$13bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b153o67bo4bo3b2ob2o3bo7bo9b3obo
12bo2b5o10bob3o4bo4b3o9b2o5bo2bo6b2obo3b3o2b2o$13b3o2bo18b2o7bo6b2o3b
3o2b3o5bo3bo4bo7bo144b2ob2o63bobo2bo2b2ob2o2bobo4bo2bo8bo4b2o10b2o3bo
4b2o5bo4bo4b3o2bobo10bobo4b2o7b3obo3b2o$13bo4bo5bo2b2o7b2o9b2o9b2o3bo
7b2obo6b6o4b141ob3o4bo61bo9bo2b2o4b2o3bo4b2o7b2o2bo7bobo4bo9b3o2b3o2b
3o2b2o12bo$14b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo131b2o2b3o2bo
67b4o3b2o4bob2o6b3o8b3o10bo3b4o6bo4b2ob2o2bo3b2o$14bobo7bo4bo5bo2b2o7b
2o9b2o9b2o3bo7b2obo6b6o4b128o3bo3b2o74b2o2bo3bo2bo2bo6bo9b3o3b3o6bobo
3b2o2bo6bo2bo2bo3bo$15bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo
122bo74b3o7bo5b2o2bo3b3o11bo4bo3b2obo6bo3bo7b2ob3o3b3o$14bo3bo6bobo7bo
4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b116o79bo2bo10b2obob4o2bo14b2obo5b
o6bo2bob3o6bo$15bo10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo
106bo3bob3o72b2o11b2o5b2ob2o14bobo14bo2bo2bo8b3o$17b2o6bo3bo6bobo7bo4b
o5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b102o4b2o2b2o86b2o4bo19bo20b2o$26bo
10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo93bo122bo$16bo11b2o6b
o3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b91o4b3o$15bo2bo18bo
10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo81b2obob2obo$27bo11b
2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b77o5bob2obo$14b2o
3bo6bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo68bo5bo$
14b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b65o2b
ob2obo$17bo7b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3b
o4bo7bo56b3o5bo$13b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o
3bo7b2obo6b6o4b52o4b2o2bo37bo5bo$14bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b4o
6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo43bo3bobo37bobo3b3o$14bo3bo5b6o
6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b40o2b
2o2b3o35bo3b4o5bo$14bo10bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo18b
2o7bo6b2o3b3o2b3o5bo3bo4bo7bo30b2o3b4o23bo2b3o8b3ob2o7bo$13b2obo8bo3bo
5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo6b6o4b
27o32bobo4bo11bobobob2obo$13bo2bo8bo10bo3bo9bo7b2o3bo6bo2bo18bo10bobo
7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3bo4bo7bo18b2ob2o39b2o2b2obob2ob2ob
4o12bo$13b5o6b2obo8bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o
9b2o9b2o3bo7b2obo6b6o4b16o2bo29b2o4bobo11b2ob2o2b6o8bobo$14bob2o6bo2bo
8bo10bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo
3bo4bo7bo12b2ob2o6b3o14b2o2bobo2bo2b2ob4o5bob2o6b3ob2obo$15b2o7b5o6b2o
bo8bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b2obo
6b6o3b3o2bo2bo4b3o5bob2o10b3obo3bo4bo4bo4b2ob3o2bo6b4o$25bob2o6bo2bo8b
o10bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o5bo3b
o3b3o2bo6b2o7b3o3b2o3bobo2bo3b3o5bo2bo5bo2b2obobo2bo6b2o$15b2o9b2o7b5o
6b2obo8bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo7b
2obo4bo4b2o3bo8b4o5b5obobo3b2ob2ob3o4bo9b2ob3o2b2o$14bob2o18bob2o6bo2b
o8bo10bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo6b2o3b3o2b3o3b
o5bo2bo7bobo2b2ob2o2b2o2bob5o5bob2o2bo13b2o5bo$13b5o8b2o9b2o7b5o6b2obo
8bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o9b2o9b2o3bo5b3o5bob
4o3bo7b6obo2bo2b2o2b3o2bobo15b2o$13bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo
9bo7b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo18b2o7bo6b2o4b2o2b2o4bobo4b3o2bo
11b2o11bo16bo$13b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo5b6o6b5o19bo11b2o6bo
3bo6bobo7bo4bo5bo2b2o7b2o9b2o10b4ob3o6bo7bo8b4o30b2o$14bo9bo2bo8bob2o
18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo18b2o9bo2b
2ob2o3bo2b3o3bobo9b2o$14bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo5b6o6b
5o19bo11b2o6bo3bo6bobo7bo4bo5bo2b2o7b2o11b2o12b3o$14bo3bo6bo9bo2bo8bob
2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo18bobo4b
o7b2ob3o70bo$13b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo5b6o6b5o19bo
11b2o6bo3bo6bobo7bo4bo5bo2b2o5b3o8bo65b2o14bobo$17bo7bo3bo6bo9bo2bo8bo
b2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo6bo2bo18bo10bobo7b4o6b3o2bo3bo11bo
3bo2b2o7b2o34bo13b3o16b2ob3o$14b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2o
bo8bo3bo5b6o6b5o19bo11b2o6bo3bo6bobo7bo4bo6bo10b3ob3o4b2o13bo22bobo14b
o7bo5b2o5b2o$14b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9b
o7b2o3bo6bo2bo18bo10bobo7b4o5b3o14b3o4b2o12b2o21bo4b2o4bob2ob2o6b3o6bo
3bob2ob2o$25b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo5b6o6b5o19b
o11b2o6bo3bo6bobo9b3o10bo2b4o2bo4bo6b2obo23bob4o7b3o14b2o3b2o$15bo2bo
6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo6bo2bo
18bo10bobo9b2o3bo7b2o2b2o4bob2o5bo8bo13b2o3bobo12b2o3b3o5b3o3bob2obo2b
obo$16bo19b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo5b6o6b5o19bo
11b2o6bo3bo5b2ob2o2b4o5bo3b2o5bo6b2o2bo2bo2bo12bo3b2o3bo2b4ob2obob4ob
2o4bob2o2b2ob2o5bo$26bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo
8bo10bo3bo9bo7b2o3bo6bo2bo18bo11bo2bobobo19b2obo5b3obo13bobo5bo3bo2bob
o3bo2b3o4bobo7bo4b2o3bo$27bo19b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2ob
o8bo3bo5b6o6b5o19bo11b2o5bobo2b2obo19b2o2b2o31b2o6b2o6b2o4b2o16b2obo$
37bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3b
o6bo2bo17bo4bobobo17b2o3bo4b2o11b2o3b3o6bo7bo6bo$38bo19b5o5b6o6bo3bo5b
2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo5b6o6b5o19bo12b2obo2bo19b2o5bobo9bo4b
4o$48bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b
2o3bo6bo2bo10bo2b6o19bo5bo6bo2bo$49bo19b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o
7b5o6b2obo8bo3bo5b6o6b5o20b2o5b2o2bo28bo2bobo2bo$59bo2bo6b2o3bo8bo7bo
3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo9bo7b2o3bo9bobo3bo32bo4bo5b4o
$60bo19b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo5b6o6b5o18bo3b2o
8bobo16b2o3b2o3b3o6bo7bo6bo$70bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bo
b2o6bo2bo8bo10bo3bo9bo10bo2bo2b2obobo3bo7bobo13b3o19b2o6b2o6b2o4b2o16b
2obo$71bo19b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo8bo3bo5b6o8bo7bo4b
o10bo7bo6bo14bobo5bo3bo2bobo3bo2b3o4bobo7bo4b2o3bo$81bo2bo6b2o3bo8bo7b
o3bo6bo9bo2bo8bob2o18bob2o6bo2bo8bo10bo3bo8bo2bo5bo2b3o5b2o3bo2bob2obo
6bo13bo3b2o3bo2b4ob2obob4ob2o4bob2o2b2ob2o5bo$82bo19b5o5b6o6bo3bo5b2ob
o7b5o8b2o9b2o7b5o6b2obo8bo3bo9b2o14bobo2b3o4bobobo9b2o10b2o3bobo12b2o
3b3o5b3o3bob2obo2bobo$92bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o18bob2o6bo
2bo8bo25bobo3bo2bobo3bo2bob2o3b2o5bo14bob4o7b3o14b2o3b2o$93bo19b5o5b6o
6bo3bo5b2obo7b5o8b2o9b2o7b5o6b2obo21bobo2b2obo6b2o2b2ob2o2b3ob2ob2o11b
o4b2o4bob2ob2o6b3o6bo3bob2ob2o$103bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o
18bob2o6bo2bo10b3o8bo3b2o3b5ob2o4bo4b2o2b2o2bo12bobo14bo7bo5b2o5b2o$
104bo19b5o5b6o6bo3bo5b2obo7b5o8b2o9b2o7b5o7bob3o8b2o2bo4b3ob3o5b2o2bo
5bobo2b3ob2o6bo13b3o16b2ob3o$114bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o
18bob2o6bo2bo15bo3bo5bo6bo8b3o3bobo22b2o14bobo$115bo19b5o5b6o6bo3bo5b
2obo7b5o8b2o9b2o8bo20b2o5b2o6bo12bo2b3o37bo$125bo2bo6b2o3bo8bo7bo3bo6b
o9bo2bo8bob2o19bobo25bobo19bo$126bo19b5o5b6o6bo3bo5b2obo7b5o8b2o10b2o
16b3o5bob2o$136bo2bo6b2o3bo8bo7bo3bo6bo9bo2bo8bob2o9b3o23bo22bobo$137b
o19b5o5b6o6bo3bo5b2obo7b5o11bo22bo2bo20bobo15b2o7bo$147bo2bo6b2o3bo8bo
7bo3bo6bo9bo2bo10b2o23b2ob3o18bo2bo16bo4bobo$148bo19b5o5b6o6bo3bo5b2ob
o10b2o27b2o17b2o15bob2o4bo$158bo2bo6b2o3bo8bo7bo3bo6bo10b3o47bo4bo8b2o
b2o6bobo$159bo19b5o5b6o6bo3bo6bo32b2o15b5o13bo3b3o3b2o9bo2bo$169bo2bo
6b2o3bo8bo7bo3bo6bo27b2o3b3o15b3o8b2o4b5o4b2ob2o7bobobo$170bo19b5o5b6o
35bobobobo17b2o10b2o3bob3o2b2obo4b2obo3b2o$180bo2bo6b2o3bo8bo7b3o27b3o
2bo19bobo2b2o5b2obo9bob6o4b2o10b2o$181bo19b5o6b4o27b3o2bo17b2o2bob2o
18bobo13b6ob3o$191bo2bo6b2o3bo4b2obobo29bob2o19b2obo20bo3b2o3b2o2b2ob
5o2b2o4b2o$192bo22bo32b2o16b2o2bo26b5o12bo4b2o13bo$202bo2bo4bo2bo32bob
o18b3o36bobo3bo3bo2b2o12b2o$203bo7bo2bo31b3o19b2o37bo4b3o5bo4bo6b2obo$
211bo2b2o30b2o74bob2o5bo8bo$212b3o108bo6b2o2bo2bo2bo$211bobo30b2o80b2o
bo5b3obo$211b3o29bo80b2o2b2o$210bo33bo79b2o3bo4b2o$210bo2bo31b3o79b2o
5bobo$211bob2o30bo2bo80bo5bo$212bo$247bo$212bo34bob2o2bo$211bob2o32bo
4b2o$210bo2bo34bobo$210bo$211b3o33bo2b2obo$211bobo33b2o2b2o2bo$212b3o
33bo5b2o$211bo2b2o$211bo2bo38b2obo$210bo2bo37b3obo$215bo$211b2obobo33b
o$212b4o36bo2b2o$212b3o35b2o2bo$251bo2b2o$255bo$253b2o2bo$253b2o3bo$
253b2o$254bo$255b2o!

Notice the dendritic forms at the corners of the greyship. Such large complicated corners were, at period 5, simply not possible a year ago. Various improvements to Amling's search program, LLSSS, including speed increases, memory reduction, the ability to detect branching and to recognize when a branch has a known solution have brought these previously intractable problems within reach.

Greystretchers Galore
Amling has recently made substantial progress in the search for "greystretchers". These are wickstretchers that can stretch a patch of stripes of extendable width. Greystretchers only stretch the stripes in one direction from a stationary base and should not be confused with spacefillers, which stretch the stripes in multiple (non-opposite) directions.

The first recent result is a new type of c/4 orthogonal greystretcher. Although a greystretcher at this speed was already known, this new stretcher has the amazing property that the wick stabilizing the sides travels at 2c/8 (that is, c/4 period-8). Normally, p8 would be too high to search for a stretcher directly, but Amling's search program, in some cases, is able to quickly convert a high-period problem into a much more tractable lower-period problem.

Code: Select all

#N c/4 orthogonal greystretcher
#O Keith Amling, 9 August 2023
#C https://conwaylife.com/forums/viewtopic.php?p=164825#p164825
x = 156, y = 145, rule = B3/S23
84bo$80b2obo5bo$78bo2b2o2b4o2b3o$75b4o4b2o6b3o$67bo2bo3bob2obo2bo2b2o$
67bo2bobob2o7b2o6bo$66b2o19bo4bobo$67bob2ob2o4bo3bo3bo6bo$67bo10b2o2bo
$67bob2ob2o4bo3bo3bo6bo$66b2o19bo4bobo$67bo2bobob2o7b2o6bo$67bo2bo3bob
2obo2bo2b2o$75b4o4b2o6b3o$78bo2b2o2b4o2b3o$80b2obo5bo$84bo2$86b2o$85bo
2$83b2o$83b2o$84bob2o$82b2o$82b2o$86b2o16bo6b2o$86b2o15bob4o2b2o$83b5o
10b3ob2o2b3o5b3o$84bobo11b2ob2o3bobo2b2o$85b3o6bo7b2o7b2o$87b3ob2o7b3o
$86bo2b2o3b2o3b2o$87b2o6b2ob3o$88bob2o5b3o$87b2o8bo$87bo$87b2o2bo$85b
2ob2o$85bo3bo$86bo3bob3o14bobo$86bo3b3obo3b2o8bo2bo$90b2ob3ob2ob2o5bo
3bo$54bobo22bo10bo2bobob2o2b2o2bobo38b2o$21b2o17bo13bo13bo9bobo14bo5b
2o2bob2obo34bobo2b3o$20b3o2bobob2o9b2o12bo2bo9bob2o4bob2o2bobobo9b2o6b
o42bo$21b2ob2o5bo7bobo4bob2o6bo4b4obo4b2o5bob4o2bo7bo4b2obo6bo39bo$16b
o7bo14bobo4bob2o5b3o2bo9b4obob2obo3b3o2b2o2b7ob2o2bo4bo6bo5bo5bo5bo5bo
4b2o7bo$7bobo4bobo9bobob2obo2b2o3bo3bo3bo9b2o3b3o8bob2o2b2o3bo5b2obo4b
obob2o2b2obo3b2o2bob2o2bob2o2bob2o2bob2o2bob2ob3o4bo$6bo2bo3bo3b2o3bo
2b2o2b2o2bo2b3ob2o2b3o2b5obobobo6bobo18bo2bo10b3o2bobob4ob4o2b4o2b4o2b
4o2b4o2b2o4bo3bo$5bo3bo2b2obo2bo4b2ob2o5bo7b2o3bo3b3o6b2o3bo4b2o3b2o
17bo6bo3bo3bo38b2o2bobo$3bobo7bo2b2o6bob2o6b2o3bo15b3o3bobobo3b3o3bob
2o13b2o7b4ob2ob38o2bobo$3b2o3bo5b3o5bo3bo12bo3b2o9b3o2b2o3bo11b4o21b2o
bo42b3ob2o$5bobo6b2ob5ob2obo13b2o13b2o20bobo25b42o$2b5o11bo6bo121bo$b
2ob2o101b40o$b2o2bo94bo2bo2bo$b2o2bo94bo2bobob40o$2b2o95b2o46bo$100bob
2ob42o$4bobo93bo$4b2o94bob2ob42o$4bo94b2o46bo$2bobo95bo2bobob40o$o2b2o
95bo2bo2bo$o3bo102b40o$obo144bo$107b40o$100bo2bo2bo$100bo2bobob40o$99b
2o46bo$100bob2ob42o$100bo$100bob2ob42o$99b2o46bo$100bo2bobob40o$100bo
2bo2bo$107b40o$obo144bo$o3bo102b40o$o2b2o95bo2bo2bo$2bobo95bo2bobob40o
$4bo94b2o46bo$4b2o94bob2ob42o$4bobo93bo$100bob2ob42o$2b2o95b2o46bo$b2o
2bo94bo2bobob40o$b2o2bo94bo2bo2bo$b2ob2o101b40o$2b5o11bo6bo121bo$5bobo
6b2ob5ob2obo13b2o13b2o20bobo25b42o$3b2o3bo5b3o5bo3bo12bo3b2o9b3o2b2o3b
o11b4o21b2obo42b3ob2o$3bobo7bo2b2o6bob2o6b2o3bo15b3o3bobobo3b3o3bob2o
13b2o7b4ob2ob38o2bobo$5bo3bo2b2obo2bo4b2ob2o5bo7b2o3bo3b3o6b2o3bo4b2o
3b2o17bo6bo3bo3bo38b2o2bobo$6bo2bo3bo3b2o3bo2b2o2b2o2bo2b3ob2o2b3o2b5o
bobobo6bobo18bo2bo10b3o2bobob4ob4o2b4o2b4o2b4o2b4o2b2o4bo3bo$7bobo4bob
o9bobob2obo2b2o3bo3bo3bo9b2o3b3o8bob2o2b2o3bo5b2obo4bobob2o2b2obo3b2o
2bob2o2bob2o2bob2o2bob2o2bob2ob3o4bo$16bo7bo14bobo4bob2o5b3o2bo9b4obob
2obo3b3o2b2o2b7ob2o2bo4bo6bo5bo5bo5bo5bo4b2o7bo$21b2ob2o5bo7bobo4bob2o
6bo4b4obo4b2o5bob4o2bo7bo4b2obo6bo39bo$20b3o2bobob2o9b2o12bo2bo9bob2o
4bob2o2bobobo9b2o6bo42bo$21b2o17bo13bo13bo9bobo14bo5b2o2bob2obo34bobo
2b3o$54bobo22bo10bo2bobob2o2b2o2bobo38b2o$90b2ob3ob2ob2o5bo3bo$86bo3b
3obo3b2o8bo2bo$86bo3bob3o14bobo$85bo3bo$85b2ob2o$87b2o2bo$87bo$87b2o8b
o$88bob2o5b3o$87b2o6b2ob3o$86bo2b2o3b2o3b2o$87b3ob2o7b3o$85b3o6bo7b2o
7b2o$84bobo11b2ob2o3bobo2b2o$83b5o10b3ob2o2b3o5b3o$86b2o15bob4o2b2o$
86b2o16bo6b2o$82b2o$82b2o$84bob2o$83b2o$83b2o2$85bo$86b2o2$84bo$80b2ob
o5bo$78bo2b2o2b4o2b3o$75b4o4b2o6b3o$67bo2bo3bob2obo2bo2b2o$67bo2bobob
2o7b2o6bo$66b2o19bo4bobo$67bob2ob2o4bo3bo3bo6bo$67bo10b2o2bo$67bob2ob
2o4bo3bo3bo6bo$66b2o19bo4bobo$67bo2bobob2o7b2o6bo$67bo2bo3bob2obo2bo2b
2o$75b4o4b2o6b3o$78bo2b2o2b4o2b3o$80b2obo5bo$84bo!

This period-reducing trick is even more astounding in the next greystretcher, which travels at c/3 orthogonally while the side stabilizations "travel" at 3c/9 (the sides actually don't move at all; they're a stable snake extension). In fact, this is the first c/3 orthogonal wickstretcher of any type!

Code: Select all

#N c/3 orthogonal greystretcher
#O Keith Amling
#C Snake-extending side component by Keith Amling, 11 August 2023
#C Shown here with new extensible line-stretching greyship
#C components by Keith Amling, 20 August 2023
#C https://conwaylife.com/forums/viewtopic.php?p=164881#p164881
#C https://conwaylife.com/forums/viewtopic.php?p=165498#p165498
x = 93, y = 197, rule = B3/S23
53bo$52bobo$51b2o3bo$52bo4bo$51b5obo$50b3o$50bo2bo$50bo2bo2$51b2o$52bo
bo$56bo$57bo$53b3o$54bo2bo$55b2o2$55bobo$52bob2obo$51bob2o$50b2ob2o$
51bob2o23bo$52bob2obo18b2o$55bobo18b2o$78bo$55b2o19bo$54bo2bo17b3o$53b
3o19bo$57bo16b2o$56bo18bo$52bobo$24bo26b2o26bo$22b2o34bo16b4o$22b2o26b
o2bo3bobo15b2o$50bo2bo3bobo15b2o$23b3o24b3o4bo16bob2o$23b3o25b3o18b4ob
o$52bo3b2o13bo5b2o$20b3o28b2o3b2obo11bob2o2b2o$20b2o29bo2bobobo11bo2bo
3b2o$52bobobo13bobobo2b2o$19b3o31b2obo12bo2bob2obo$18bo2bo30bob2o13b3o
4b3o$19b2o29b2o3bo21bo$22b3o25bo2bo3bo12b2o5b2o$19bob2o26b2ob2obobo12b
3ob2o$19bo4bo25bo25b2obo$19bob3o27b2o4bo12b2obo3b3o$22bobo31b2o12b2o4b
o$19b2o32b2obo16bo2b4o$18bo2bobo32b2o12b2o5bobo$19b3obo28b2obo2bo11b4o
bo$22bo28bo3b2o12bo2bo$20b2o28bo4bo8b2o3bo2bo$20b3o20b2o6bo3bo7b3o3b3o
$36b3o2b2o3bo6bo3bo2b2o2b2o$4bo18bob2obo7b2o3b2obobo4b2o4bo2bo2b2o$2b
2o18b2ob2obob2o6bo6bo5b2o4bobo3b2o5b3o$2b2o17bo14bo4bob2o8bo10b4obo2bo
$4bo15b9o3bobo8b5o8b2obob2obo7bo$2bo16bo13b2ob2obob3o2bo9b2o3bo4bobo3b
o$b3o4bo2b2o5b2ob2o2b8o5bo2bo4bo2bo2b3obo4bobo2bobobobobo$bo4b2o3b2o6b
o2b3o3bo4b5o3b2o2bo3b2o5bobob2o2bo2b2obo4bobob2ob2ob2ob2ob2o$2o4b2o6bo
3b3obo2b3ob5o5b2o10bobobo3bo4bo2b2obob2obob2ob2ob2ob2ob2obo$bo6b5o5bo
2b2o3b2obo2b2o3b2o2bo9bobo2bo10bo3bo$2b2o2bo3bo2b2obobo3bo2b3o2b2obo2b
ob2o3b2o6bo10b2o4b3o2bob17o$11bo10b2o2b2o7bo6bo2bo5bo2bo6bo8bo3bo17bo$
4b2o6bobo8bo3bo14b3o2bo12bo2bo7b3ob17o$13bo10bob3o13bo2bo3bobob2o6bobo
7b2o$27b2o14b2o3b2obo10bo10b19o$92bo$41bo29b21o$40bobo26b2o$39b2o24b2o
b2o2b20o$41bo15b3o2bob4obobo20bo$39b2o18bobo7b2ob20o$39b3o13bo2bo2bo5b
o3bo$45bo8bobobo2bo6b24o$40bobo2bobo6bo3bo7bo25bo$40b3o2b2o7bobob5o3b
26o$56bo7bo$43b6o4b2o2b35o$43bo4bo4bobo36bo$42b2obobo4bob38o$43bo4bobo
$44b2o2bo3b40o$92bo$44b2o2bo3b40o$43bo4bobo$42b2obobo4bob38o$43bo4bo4b
obo36bo$43b6o4b2o2b35o$56bo7bo$40b3o2b2o7bobob5o3b26o$40bobo2bobo6bo3b
o7bo25bo$45bo8bobobo2bo6b24o$39b3o13bo2bo2bo5bo3bo$39b2o18bobo7b2ob20o
$41bo15b3o2bob4obobo20bo$39b2o24b2ob2o2b20o$40bobo26b2o$41bo29b21o$92b
o$71b21o$45bo5bo12b3o2b2o$44bobo2b2obo11b3o2b3ob19o$44bo2bo7bobo8bobo
3bo19bo$44bob3o3bobob4o4bo3b3ob2ob17o$50bobo10bo3bo4bobo$43b2ob3obo12b
o3bo2bo4b17o$44bo4bob2o6bo5bo2bo2b4o17bo$44b2o2b5o6b5obo5bo2b18o$45bo
3bo3bo2bo2b3o10bo$46b4o3bobo16b20o$92bo$46b4o3bobo16b20o$45bo3bo3bo2bo
2b3o10bo$44b2o2b5o6b5obo5bo2b18o$44bo4bob2o6bo5bo2bo2b4o17bo$43b2ob3ob
o12bo3bo2bo4b17o$50bobo10bo3bo4bobo$44bob3o3bobob4o4bo3b3ob2ob17o$44bo
2bo7bobo8bobo3bo19bo$44bobo2b2obo11b3o2b3ob19o$45bo5bo12b3o2b2o$71b21o
$92bo$27b2o14b2o3b2obo10bo10b19o$13bo10bob3o13bo2bo3bobob2o6bobo7b2o$
4b2o6bobo8bo3bo14b3o2bo12bo2bo7b3ob17o$11bo10b2o2b2o7bo6bo2bo5bo2bo6bo
8bo3bo17bo$2b2o2bo3bo2b2obobo3bo2b3o2b2obo2bob2o3b2o6bo10b2o4b3o2bob
17o$bo6b5o5bo2b2o3b2obo2b2o3b2o2bo9bobo2bo10bo3bo$2o4b2o6bo3b3obo2b3ob
5o5b2o10bobobo3bo4bo2b2obob2obob2ob2ob2ob2ob2obo$bo4b2o3b2o6bo2b3o3bo
4b5o3b2o2bo3b2o5bobob2o2bo2b2obo4bobob2ob2ob2ob2ob2o$b3o4bo2b2o5b2ob2o
2b8o5bo2bo4bo2bo2b3obo4bobo2bobobobobo$2bo16bo13b2ob2obob3o2bo9b2o3bo
4bobo3bo$4bo15b9o3bobo8b5o8b2obob2obo7bo$2b2o17bo14bo4bob2o8bo10b4obo
2bo$2b2o18b2ob2obob2o6bo6bo5b2o4bobo3b2o5b3o$4bo18bob2obo7b2o3b2obobo
4b2o4bo2bo2b2o$36b3o2b2o3bo6bo3bo2b2o2b2o$20b3o20b2o6bo3bo7b3o3b3o$20b
2o28bo4bo8b2o3bo2bo$22bo28bo3b2o12bo2bo$19b3obo28b2obo2bo11b4obo$18bo
2bobo32b2o12b2o5bobo$19b2o32b2obo16bo2b4o$22bobo31b2o12b2o4bo$19bob3o
27b2o4bo12b2obo3b3o$19bo4bo25bo25b2obo$19bob2o26b2ob2obobo12b3ob2o$22b
3o25bo2bo3bo12b2o5b2o$19b2o29b2o3bo21bo$18bo2bo30bob2o13b3o4b3o$19b3o
31b2obo12bo2bob2obo$52bobobo13bobobo2b2o$20b2o29bo2bobobo11bo2bo3b2o$
20b3o28b2o3b2obo11bob2o2b2o$52bo3b2o13bo5b2o$23b3o25b3o18b4obo$23b3o
24b3o4bo16bob2o$50bo2bo3bobo15b2o$22b2o26bo2bo3bobo15b2o$22b2o34bo16b
4o$24bo26b2o26bo$52bobo$56bo18bo$57bo16b2o$53b3o19bo$54bo2bo17b3o$55b
2o19bo$78bo$55bobo18b2o$52bob2obo18b2o$51bob2o23bo$50b2ob2o$51bob2o$
52bob2obo$55bobo2$55b2o$54bo2bo$53b3o$57bo$56bo$52bobo$51b2o2$50bo2bo$
50bo2bo$50b3o$51b5obo$52bo4bo$51b2o3bo$52bobo$53bo!

With 2c/8 and 3c/9 greystretchers complete, the next target was clear: a 4c/10 (i.e., 2c/5 period-10) stretcher. This time, the side stabilization is just a row of blocks:

Code: Select all

#N 2c/5 greystretcher
#O Keith Amling, 26 August 2023
#C https://conwaylife.com/forums/viewtopic.php?p=165834#p165834
x = 186, y = 139, rule = B3/S23
133bo8bo$132b3o2bo4bo$133bo2b2o2bo$137bob2ob2o$124b3o5bo2bo3bo3b4o$
106b2o6bo5b3o2bob5o7b2o3b3o$6b3o94b2obo6b2o4b2o4bob5obo5bo2b4o$6bo2b3o
90bobob2o4bob6o4b2o4b3o7b2ob2o$6b5o90b2o3bo4b2o5b2o9bo10b2o$9b2o91bobo
b3o2bo2bo2bo8bobo13b2o$2b2o15b3o81b2o8bo13bo$2bobo7b2o3bo4bobo64bobo
15b3o8b2o$2bob2o3bob3o3bo5bo64bo2bo5bob2o10bo5bob3o$3bo6bo4b2o58bobo2b
3o4b3o5b4o3b2o12bo3b3o$4b12o2bobo52b5o9bobo4bo6b3ob2o10bobo$17bo5b4obo
43bo6b2o5bobo4bob2o4b2o15bo$2b13ob4o3b2o2bo43bobob4o4b2o2b2o4bobo$bo
14b2o5b2o3bo42bo3bo3bo3bo3bo5b2o$obob8o13bo45b2ob5o4bo2b3o9b3o6bo4bo
27bo36bo$o3bo5bobo64b2o2b2obo3b2o7bo2bo4b5o5bo10bo13bo3b2o8b2obo2bo8bo
6bo$2ob4obo72b2o3b2ob2o5bo3bo4b2ob3obo12b4o9bobo3b2o6bo3bobo5b2o4bo4b
2o$6bob2o2bo68b2o3b5o4b3obo4bobo6bob2ob3o3bo4bob2o4bo9b2o3bo10bo5b2o5b
2o$7bo3bo82bobo3bob3o4b2o3bo4b6o8bob2obo5b2o3bobo3b2o2bo3bo2b3o2bob7o$
93b2obo3bo3bobo4bob2obo4b2obo4b2ob2ob2ob2o3b2o4bo2b5o2b4o4bo2bobo5b2ob
o$7bo3bo32b2o42b2o4bobo4bo2bob2ob5o4b2ob2obo7b2o7b2o6bo7bobo5bo2bo3bo
4bobobo$6bob2o2bo31b4o40b2o7bo6bo9b3obob2o2bo8bob3o3bob3o12bo5bob4o8b
2o3bo$2ob4obo34bo3bo39bo6bo9b3o3b2o4b3o4b2o9b4obo5bo2bo4b2o3b2o7b2o4b
2o5bo2bo$o3bo5bobo15b2obo9bo2b2o42b4o2bo11bo11bo4bo11bo4b4o9bo2bo17bob
o3bo$obob8o16b5o7b2o2b2o42b2obob2o2bo21b2obo30bo3bo3bo13bo6b4o$bo12bob
o10bo3b2o3bo2bo9bo41b2ob2o25bo32bo2bo2bo22b2o$2b13obo11b2o5bo3b12o42b
3o52b2o$28b2o5bo15bo2bo35bo3bo13bo21bo15bo2bo$2b13obo18b20o34b3o2bo13b
obo8bo9bobo14bo$bo12bobo9b2o8bo19bo2bo29b2o13b2o2bo2bo6bob2o6b2o2bo12b
o3bo$obob8o8bo3b2ob2o7b24o3bo23bo15b2o6b2o3b2o4b2o2bo5bo8bo3b5o$o3bo5b
obo6b2o3bo3bo3bo31bo2bo19b4o13bo2bo2bo2bobobobo6bob2o2b2o6b2o2bo2b3o$
2ob4obo9b2o4bo4bo2bo2b30o2bo20b2o3bo7b2obobobob2o4b2o4b2o2bobo10bo4b2o
3b2o$6bob2o2bo6b2obo6bobo37bob2o24b6obob3o4bobo8bo5b2ob2o4b2o2b2obo2b
3o$7bo3bo8b6o3bob42o16bo5b2o11bo4bobo2bo2bo6bo4b2o4bo6b2ob3o$27bo48bo
12b2obobo3bob3obo4b4o7b3o5b3o3b3o3bo8b2o$7bo3bo6b60o11b2ob2o5b2o3bo8bo
bo19b2o$6bob2o2bo4b2o59bo2bo12bo2bo3b2o$2ob4obo7b2o2b6ob3ob3o2b46o7bob
ob2o$o3bo5bobo6bo3bobo4b2o2bobo46bo2bob2o6bo$obob8o4bo2b3o4b4o5bo2bob
47ob2o3b2o5b2o$bo13bob5o6bo5b5o3bo48bo6bo4bo2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o$2b14ob2o4b3ob2o
2bo2bo3bobo2b51ob6ob2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o$4bo19bo2b2ob2o3bo2bobo3bo$6b14o3bo3bo
2bo4bo2bobob2o3b137o$5bo21bo2bo9bo5bo137bo$6b14o3bo3bo2bo4bo2bobob2o3b
137o$4bo19bo2b2ob2o3bo2bobo3bo$2b14ob2o4b3ob2o2bo2bo3bobo2b141o$bo13bo
b5o6bo5b5o3bo141bo$obob8o4bo2b3o4b4o5bo2bob144o$o3bo5bobo6bo3bobo4b2o
2bobo$2ob4obo7b2o2b6ob3ob3o2b148o$6bob2o2bo4b2o165bo$7bo3bo6b166o2$7bo
3bo6b166o$6bob2o2bo4b2o165bo$2ob4obo7b2o2b6ob3ob3o2b148o$o3bo5bobo6bo
3bobo4b2o2bobo$obob8o4bo2b3o4b4o5bo2bob144o$bo13bob5o6bo5b5o3bo141bo$
2b14ob2o4b3ob2o2bo2bo3bobo2b141o$4bo19bo2b2ob2o3bo2bobo3bo$6b14o3bo3bo
2bo4bo2bobob2o3b137o$5bo21bo2bo9bo5bo137bo$6b14o3bo3bo2bo4bo2bobob2o3b
137o$4bo19bo2b2ob2o3bo2bobo3bo$2b14ob2o4b3ob2o2bo2bo3bobo2b141o$bo13bo
b5o6bo5b5o3bo141bo$obob8o4bo2b3o4b4o5bo2bob144o$o3bo5bobo6bo3bobo4b2o
2bobo$2ob4obo7b2o2b6ob3ob3o2b148o$6bob2o2bo4b2o165bo$7bo3bo6b166o2$7bo
3bo6b166o$6bob2o2bo4b2o165bo$2ob4obo7b2o2b6ob3ob3o2b148o$o3bo5bobo6bo
3bobo4b2o2bobo$obob8o4bo2b3o4b4o5bo2bob144o$bo13bob5o6bo5b5o3bo141bo$
2b14ob2o4b3ob2o2bo2bo3bobo2b141o$4bo19bo2b2ob2o3bo2bobo3bo$6b14o3bo3bo
2bo4bo2bobob2o3b137o$5bo21bo2bo9bo5bo137bo$6b14o3bo3bo2bo4bo2bobob2o3b
137o$4bo19bo2b2ob2o3bo2bobo3bo$2b14ob2o4b3ob2o2bo2bo3bobo2b51ob6ob2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o$bo13bob5o6bo5b5o3bo48bo6bo4bo2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o$obob8o4bo2b3o4b4o5bo
2bob47ob2o3b2o5b2o$o3bo5bobo6bo3bobo4b2o2bobo46bo2bob2o6bo$2ob4obo7b2o
2b6ob3ob3o2b46o7bobob2o$6bob2o2bo4b2o59bo2bo12bo2bo3b2o$7bo3bo6b60o11b
2ob2o5b2o3bo8bobo19b2o$27bo48bo12b2obobo3bob3obo4b4o7b3o5b3o3b3o3bo8b
2o$7bo3bo8b6o3bob42o16bo5b2o11bo4bobo2bo2bo6bo4b2o4bo6b2ob3o$6bob2o2bo
6b2obo6bobo37bob2o24b6obob3o4bobo8bo5b2ob2o4b2o2b2obo2b3o$2ob4obo9b2o
4bo4bo2bo2b30o2bo20b2o3bo7b2obobobob2o4b2o4b2o2bobo10bo4b2o3b2o$o3bo5b
obo6b2o3bo3bo3bo31bo2bo19b4o13bo2bo2bo2bobobobo6bob2o2b2o6b2o2bo2b3o$o
bob8o8bo3b2ob2o7b24o3bo23bo15b2o6b2o3b2o4b2o2bo5bo8bo3b5o$bo12bobo9b2o
8bo19bo2bo29b2o13b2o2bo2bo6bob2o6b2o2bo12bo3bo$2b13obo18b20o34b3o2bo
13bobo8bo9bobo14bo$28b2o5bo15bo2bo35bo3bo13bo21bo15bo2bo$2b13obo11b2o
5bo3b12o42b3o52b2o$bo12bobo10bo3b2o3bo2bo9bo41b2ob2o25bo32bo2bo2bo22b
2o$obob8o16b5o7b2o2b2o42b2obob2o2bo21b2obo30bo3bo3bo13bo6b4o$o3bo5bobo
15b2obo9bo2b2o42b4o2bo11bo11bo4bo11bo4b4o9bo2bo17bobo3bo$2ob4obo34bo3b
o39bo6bo9b3o3b2o4b3o4b2o9b4obo5bo2bo4b2o3b2o7b2o4b2o5bo2bo$6bob2o2bo
31b4o40b2o7bo6bo9b3obob2o2bo8bob3o3bob3o12bo5bob4o8b2o3bo$7bo3bo32b2o
42b2o4bobo4bo2bob2ob5o4b2ob2obo7b2o7b2o6bo7bobo5bo2bo3bo4bobobo$93b2ob
o3bo3bobo4bob2obo4b2obo4b2ob2ob2ob2o3b2o4bo2b5o2b4o4bo2bobo5b2obo$7bo
3bo82bobo3bob3o4b2o3bo4b6o8bob2obo5b2o3bobo3b2o2bo3bo2b3o2bob7o$6bob2o
2bo68b2o3b5o4b3obo4bobo6bob2ob3o3bo4bob2o4bo9b2o3bo10bo5b2o5b2o$2ob4ob
o72b2o3b2ob2o5bo3bo4b2ob3obo12b4o9bobo3b2o6bo3bobo5b2o4bo4b2o$o3bo5bob
o64b2o2b2obo3b2o7bo2bo4b5o5bo10bo13bo3b2o8b2obo2bo8bo6bo$obob8o13bo45b
2ob5o4bo2b3o9b3o6bo4bo27bo36bo$bo14b2o5b2o3bo42bo3bo3bo3bo3bo5b2o$2b
13ob4o3b2o2bo43bobob4o4b2o2b2o4bobo$17bo5b4obo43bo6b2o5bobo4bob2o4b2o
15bo$4b12o2bobo52b5o9bobo4bo6b3ob2o10bobo$3bo6bo4b2o58bobo2b3o4b3o5b4o
3b2o12bo3b3o$2bob2o3bob3o3bo5bo64bo2bo5bob2o10bo5bob3o$2bobo7b2o3bo4bo
bo64bobo15b3o8b2o$2b2o15b3o81b2o8bo13bo$9b2o91bobob3o2bo2bo2bo8bobo13b
2o$6b5o90b2o3bo4b2o5b2o9bo10b2o$6bo2b3o90bobob2o4bob6o4b2o4b3o7b2ob2o$
6b3o94b2obo6b2o4b2o4bob5obo5bo2b4o$106b2o6bo5b3o2bob5o7b2o3b3o$124b3o
5bo2bo3bo3b4o$137bob2ob2o$133bo2b2o2bo$132b3o2bo4bo$133bo8bo!

This is especially impressive, as the first known 2c/5 wickstretcher of any type was found only a few months ago (see NewLifeCA issue #39). With these new greystretchers, we now have greystretchers at every speed for which we have greyships.

-- Matthias Merzenich
---endquote---

[dvgrn]

NewLifeCA #43, 3 December 2023: ever yet more superer diehards, new toggle conduits, engine-collecting, and a new knightship caterpillar

Suddenly it has been over three months since the last NewLifeCA bulletin.  It's hard to get caught up properly after such a long hiatus, but I'll give it a try.  Hopefully the LifeWiki news-archive link below will fill in most of the major gaps for anyone who is interested -- and possibly somebody will email me back with any really unwarranted missing items.

Quick reminder -- NewLifeCA back issues are kept on the conwaylife.com forums, as usual, and there's also a NewLifeCA discussion thread.

Engineered diehards
The progress of the ongoing engineered-diehard exploration -- patterns that last as long as possible, rather arbitrarily limited in this latest cycle of optimization to bounding boxes of no more than 10,000 cells -- was very difficult to keep up with for a while. It seems to have settled down for the moment.  The lifespan of the most recent design exceeds 17^^^3 in Knuth's up-arrow notation.

There's a timeline in the engineered-diehards LifeWiki article, which hopefully will collect a few more handy links as time goes on.

Non-Engineered Diehards
A new record for an asymmetric diehard from a 16x16 soup showed up a few days ago -- first new record in that category for a couple of years:

Code: Select all

#C https://catagolue.hatsya.com/hashsoup/C1/c_RoFPGCkAIf8x484318999/b3s23
#C -- a new "C1" entry in https://catagolue.hatsya.com/object/messless_14h/b3s23
#C Dies out after 1,413 ticks.
x = 16, y = 16, rule = B3/S23
2obo3bo2bob2o$bo4bob2o2bobo$2o2b3o2bo2bob2o$2b2obo3b2ob3o$8bob2o2b2o$
2bo2b3o3b2o$2b3o3bo3bo2bo$b4obo2b4ob2o$bo2bo2b5o3bo$bo3b7o3bo$b2obobob
3o2b3o$2o2bobob3ob4o$bo2b4obobobobo$2obo2bobobobo2bo$4o2b3ob2o3bo$3bob
5o2b3o!

That's a long way from the current record for diehards found in *all* Catagolue soups, though.  Symmetric soups seem to produce much longer-lasting diehards than asymmetric soups, on average -- the C4_4 symmetry in particular.  For example, there's a 4-way rotationally symmetric soup that is equivalent to the following pattern at T=155, which then goes on for another 2,345 ticks before dying out completely:

Code: Select all

#C T=155 equivalent for the current longest-lasting symmetric soup
#C (C4_4 symmetry,  https://catagolue.hatsya.com/object/messless_25h/b3s23 )
#C https://catagolue.hatsya.com/hashsoup/C4_4/c_weesMVzfE3FA144677131/b3s23
x = 66, y = 66, rule = B3/S23
40b3o$40bo$40b3o6$12bo$11bobo14b3o$10bo2bo41bo$11b2o41bobo$54bo2bo$55b
2o10$obo24b2o$obo24b2o$3o2$41b2o$41b2o13bo$56bo$56bo5$9bo$9bo$9bo13b2o
$23b2o2$63b3o$37b2o24bobo$37b2o24bobo10$9b2o$8bo2bo$9bobo41b2o$10bo41b
o2bo$35b3o14bobo$53bo6$23b3o$25bo$23b3o!

Safe Glider Toggles
A couple of new elementary "input-safe" toggle conduits have appeared recently.  These are mechanisms that create a still life when a glider strikes them -- and then cleanly remove that still life if another glider is sent in on the same path.  The still life can also be removed by a glider coming in at 90 degrees.  Here are block and beehive factories with this property:

Code: Select all

#C block toggle factory (left):  Luke Kiernan, 9 October 2023
#C beehive toggle factory (right): Mitchell Riley, 16 November 2023
x = 138, y = 71, rule = B3/S23
69bo$68bo$68b3o14$91bo$92bo$90b3o3$126bo$125bo$125b3o4$bo$2bo$3o3$120b
o$119bobo$119bobo$120bo4$114bo$14bo100bo$15bo97b3o$13b3o2$32b2o$32b2o
2$133b2o$131bo2bo$131b3o2$21b2o98b2o8b2obob2o$21b2o98b2o9bob2obo$115b
2o15bo$116bo7b2o3b2obo$113b3o7bo2bo3bob2o$113bo8bob2o3bo$122bo5bo$123b
6obo$125bo3bobo$30b2o5b2o89bo2bo$29bo2bo4bobo89b2o$25b2o3bobo6bo$21b2o
bobo4bo7b2o$22bobo9b2o$21bo2b2o8bo$22b2o11b3o$24b2o11bo$24bo$25bo$24b
2o!

The G-to-beehive converter can be extended by adding a transparent beehive, producing quite a number of possible outputs.  For a lot more details see this "G-to-X" LifeWiki article.

Confirmed Minimum Spaceships
Keith Amling has been working through a series of searches to confirm that, for example, 64P2H1V0  and 37P4H1V0 and 30P5H2V0 are the smallest possible spaceships with their respective periods and speeds -- and also turned up a few new (non-minimum) c/3 spaceships:

Code: Select all

#N 6 new c/3 spaceships
#O Keith Amling, 12 November 2023
#C found via "some extremely sketchy hacks for LLSS" that allow
#C   for exhaustively searching for all spaceships below a set population.
#C  https://conwaylife.com/forums/viewtopic.php?p=171031#p171031  
x = 81, y = 55, rule = B3/S23
11bo24b3o26bo$10b4o17b2ob2obo23b3ob2o3b3o$9bo3b2ob2o13b2o4bob2o19bo12b
o$7bo5bo2b2o12bo2bo3bobobob3o15b2o3b4o2bo$5b3o7bo2bo18bobobo4b2obo16bo
3bo$b2ob2o3bo9bo15bo4b2o2bo3b3o13b2ob2o$b2o2bo2bo28b2o4bo3bo3bo11bobo
2bo$o2bo13b3o14bo4bo10bo10b3obo4bo3bo$20bo3bo9b2o3bo20b2obo5bo2b4o$22b
4o33bo3bo8bo3bo$22bo3bo9b3o31bo2bobo$20bo2bobo45bo$21bo8$37b2o26b4o$
34b2obob2o22b3ob2o3bo$31b4o2bo4bo19b2o6b3ob3o$30bo4bo6b3o16bo3bo2bobo
6bo$31b2o7bo3b2ob2o13b2o4bo2bo3b2o$40b2o2bo2b2o13b4o$37b2o7bo2bo10b2o$
34b2ob2o27bo$31b4o2b2o21bo5bo$30bo4bo31bo$31b2o31b2o2b2o$66b3o$66b3o8$
65bo$61b3ob3o$60bo6b2o$61b2o3bo2bo5b3o$71bob2o3bo$71b2o3bobo$69bo3bo4b
2o$78b3o$76bobo$75b2o$70bo3bo2bo$69b4o$68bo3bo$69bobo2bo$73bo!

New c/4 Rakes and Puffers
A lot of new lower-period c/4 rake technology has been invented recently, all still too big to quote here but much smaller than previous designs.  In the first half of November a series of improvements to c/4 diagonal rakes by Keith Amling, praosylen, EvinZL, and May13 created a series of period-116 c/4 rakes and spaceships.  David Bell then picked up and extended these improvements to build a variety of puffers and higher-period mechanisms in several following posts.

Oscillator Engines
Expertise is continuing to develop about construction methods for novel oscillator engines, along with writing and running search programs to help dig up new examples.  Here are a few of these from the last couple of months, just to give the flavor of the variety of mechanisms that the oscillator construction exports have learned how to work with.

More details and more new engines can be found in links in the LifeWiki news archive for November 2023.

Code: Select all

#N P41 pi-heptomino hassler
#O Nico Brown, 20 October 2023
#C New smallest known period-41 oscillator
#C https://conwaylife.com/wiki/P41_pi-heptomino_hassler
x = 55, y = 34, rule = B3/S23
6b2o16bo$5bobo14b3o$b2o2bo10bo4bo3b2o$bobob2o7b3o3bob2o3bo$3bo9bo6bob
ob3o$3b4o6b2o4b2obobo$b2o3bo16bo$o2b3o22b2o$2obo24bobo$3bo3b3o3b3o6bo
6bo$3b2o16b2o$11bo8bo$11bo9b2o$6b2o3bo10bo$5bobo$5bo$4b2o$49b2o$49bo$
47bobo$32bo10bo3b2o$32b2o9bo$34bo8bo$32b2o16b2o$25bo6bo6b3o3b3o3bo$24b
obo24bob2o$25b2o22b3o2bo$31bo16bo3b2o$30bobob2o4b2o6b4o$28b3obobo6bo9b
o$27bo3b2obo3b3o7b2obobo$28b2o3bo4bo10bo2b2o$30b3o14bobo$30bo16b2o!

Code: Select all

#N period 81 pi-heptomino hassler
#O Luke Kiernan, Carson Cheng, iNoMed -- 12 October 2023
#C Luke Kiernan 2022 partial 6 July 2022, Carson Cheng p27 sparker 15 August 2022;
#C  completed by iNoMed, 12 October 2023
x = 86, y = 75, rule = B3/S23
6bob2o4b2obo$6b2o2bo2bo2b2o$4b2o3bo4bo3b2o$3bo3b2ob4ob2o3bo$4b3obobo2b
obob3o$6bobobo2bobobo$9bo4bo$10bo2bo$10bo2bo2$7b2o6b2o$7bo8bo$8b2o4b2o
$10bo2bo50bob2o4b2obo$6b12o46b2o2bo2bo2b2o$5bo12bo43b2o3bo4bo3b2o$6b4o
4b4o19b2o22bo3b2ob4ob2o3bo$37b2o23b3obobo2bobob3o$6b3o6b3o46bobobo2bob
obo$5bo2bo6bo2bo48bo4bo$5b2o2b6o2b2o49bo2bo$68bo2bo2$65b2o6b2o$9bo55bo
8bo$10bo15b2o38b2o4b2o$10bo15b2o40bo2bo$8b2o23bo30b12o$8b2o21b2obo28bo
12bo$2o27b2o4bo28b4o4b4o$o2bo17bo8b5o$6bo17b2o5bo23b2o7b3o6b3o$bo2bo
20b2o28bo7bo2bo6bo2bo$3b2o13b2o4b2o27bobo7b2o2b6o2b2o$18b2o4b2o27b2o$
17bo40bo$17bo6b2o32b3o$18bo5bo36bo5bo$25b3o32b2o6bo$27bo40bo$31b2o27b
2o4b2o$9b2o2b6o2b2o7bobo27b2o4b2o13b2o$9bo2bo6bo2bo7bo28b2o20bo2bo$10b
3o6b3o7b2o23bo5b2o17bo$51b5o8bo17bo2bo$10b4o4b4o28bo4b2o27b2o$9bo12bo
28bob2o21b2o$10b12o30bo23b2o$14bo2bo40b2o15bo$12b2o4b2o38b2o15bo$11bo
8bo55bo$11b2o6b2o2$14bo2bo$14bo2bo49b2o2b6o2b2o$13bo4bo48bo2bo6bo2bo$
10bobobo2bobobo46b3o6b3o$8b3obobo2bobob3o23b2o$7bo3b2ob4ob2o3bo22b2o
19b4o4b4o$8b2o3bo4bo3b2o43bo12bo$10b2o2bo2bo2b2o46b12o$10bob2o4b2obo
50bo2bo$70b2o4b2o$69bo8bo$69b2o6b2o2$72bo2bo$72bo2bo$71bo4bo$68bobobo
2bobobo$66b3obobo2bobob3o$65bo3b2ob4ob2o3bo$66b2o3bo4bo3b2o$68b2o2bo2b
o2b2o$68bob2o4b2obo!

Code: Select all

#N 44P49
#O Mitchell Riley, 14 November 2023
#C New smallest known oscillator of period 49
x = 39, y = 13, rule = B3/S23
o18b2o$3o16b2o$3bo$2b2o$26b2o$14bo12bo6b2o$3b2o8b3o7b3o8b2o$3b2o6bo12b
o$11b2o$35b2o$35bo$18b2o16b3o$18b2o18bo!

Half-Baked Knightship Caterpillar
And last but not least -- yesterday, with no advance warning (that I noticed anyway), FWKnightship produced an example of the long-awaited HBK caterpillar -- a period-1024 engineered knightship caterpillar macro-spaceship.

A reasonably detailed explanation of the pattern can be found in the HBK caterpillar LifeWiki article. Most of the support mechanisms are completely new, not copied from previous HBK variants, so it's definitely worth a look!

Keep the cheer,

Dave

Here's a reply from Dean Hickerson that brings up an interesting point:

A new record for an asymmetric diehard from a 16x16 soup showed up a few days ago -- first new record in that category for a couple of years:
...
#C Dies out after 1,413 ticks.

That's not quite the best known 16x16.  I posted one that lasts 1456 gens in September.

Code: Select all

x = 16, y = 16, rule = B3/S23
4o2bo5bo$3b3o5b2o$8b2o4bo$o2b3o2bo3bo2bo$2o2bo6b3o$o3bobo6bo$bo2b2o9bo
$b2ob2o3bobo3bo$3obo4b3o3bo$8b2o3b2o$12bob2o$10b4o$2b2o4bobob4o$2bo6bo
3b3o$3bo3b2obo3bo$2b2o4b3ob3o!

Dean Hickerson

What Dean says is true -- and what I said is also true, at least in the sense that I meant it!  Dean's pattern above is the current record for 16x16 patterns.  The Catagolue discovery lasting 1413 ticks is the current record for 16x16 soups.

The terminology that has been used consistently for the last several years of Catagolue/apgsearch soup searching is that

• a "soup" is an initial pattern of some size (not necessarily 16x16) that can be clearly shown to have been generated randomly.
• a "naturally occurring" pattern is one that has appeared in a census of final outcomes from a C1 (asymmetric) soup -- or that in very rare cases has appeared temporarily in such a soup but then was destroyed again;
• similarly, a "semi-natural" pattern is one that has been censused from a symmetric soup.

 In Catagolue's case, there's a known SHA-256 pre-image for every C1 soup.  It's technically not impossible that SHA-256 has some flaw that would allow a pre-image to be created for some non-random 16x16 pattern, like Dean's example above, or the 16x16 pattern that has a 2-engine Cordership in its census -- see the note at the bottom of the LifeWiki 2-engine Cordership article.

However, anyone who solves that SHA-256 preimage problem will likely be capable of breaking some much more significant records than the longest-lasting natural C1 diehard in Conway's Life ... so nobody worries too much about that possibility!  If a pattern has a SHA-256 preimage, we can safely assume that it's a random soup.

Statistically speaking, it's clear that 2-engine Corderships and lots of other highly improbable Life objects will eventually become officially "natural" if enough soups are searched.  So far that hasn't happened.

Keep the cheer,

Dave

[dvgrn]

NewLifeCA #44, 9 December 2023: c/3 wick ship and greyship, c/5 diagonal wickstretcher, new c/2 and 3c/7 rake periods

This is another NewLifeCA guest post by Matthias Merzenich -- thanks again, Matthias!

Some of the quoted RLE below is longer than I usually venture to send in NewLifeCA emails these days. I removed one chunk of RLE at the top that would have taken a lot of scrolling to get past and find the rest of the writeup. The online version of this episode may be more convenient to read. (EDIT: this is an online version, so I didn't leave out any RLE here.)

Keep the cheer,


Dave

Matthias writes:

---beginquote---

Period-6 c/3 Wick Ship

Keith Amling has continued to use his spaceship search tools to great effect. Recall that one powerful feature is the ability to reduce a higher period problem to a lower period problem. In this new example the front end for a 2c/6 wick is reduced to a period-3 problem and then solved at the lower period:

Code: Select all

#C A c/3 spaceship containing a 2c/6 wick
#C Front end by Keith Amling, September 6, 2023
#C Wick and back end by Hartmut Holzwart, January 24, 2022
#C https://conwaylife.com/forums/viewtopic.php?p=166490#p166490
#C https://conwaylife.com/forums/viewtopic.php?p=140693#p140693
x = 111, y = 200, rule = B3/S23
67bo3bo$64bobob2ob3o$63bo2bo6b2ob2o$58b2o2b2o2bo3bo2bo2b2o$58b2obob2o
2bo2bo4bo2bo$57bo3bo4b2o$57bobobo2bo2b2o$66bo$58b3o3$59b2o$58bo2bo3bo$
59bobo2bobo$60b2obo3bo$61bobob2o$59bobo$58b2o$56b2o3bo$59bobo$61b2o$
58b2o2bob2o$32b3o14bo8bo3bo3bo$2bob2o13b2o10bo15b4o10b2o4bo$b2ob2ob2ob
o7b2o9b3o5bo8b2o3bo7b2obo4bo$o2bobob2ob2o6b2ob2obo3bo2bob3ob2o6bo4bo8b
2o$bo6bo3bo2b4o2bo2b2obo3bo4bo2bo5bobo12b2ob3o$10bob4o5bo4b4ob2o3bo2bo
2b2o3b2o10bo6bo$13bo4bo8bo2b3o9bo4b2o9b4obobo$11b2o12b2o2b2o2b5obo2bob
2o2b2o7bo3bo$37bob2o8bob3o7bobo$48bo5bo4bo$50b2o3bo4bo$49b3o5b2ob2o$
23b2o13bo13b2ob2obob2o$21b3obo3b3o5bobo5b3o4b2o6bo$17b2ob2o3b2obo7bo3b
o7bo4b2o2bo$17b2o2bo2bob3o4bob3ob3obo4b3obo9b2o8b3o6b2o$16bo2bo6b2o4b
2obo5bob2o4bo6b3o4bo6b2obobo2b2obob2o$29bob2ob2ob3ob2ob2obo2bob2o3bo3b
o7bobobobo2bo2bobob3o$29bo8bo8bo12b3ob2o3b2obo2b2obo2bob2o$30bo2b2o2bo
bo2b2o2bo11b3obob2o8bo3bobo2bob2ob2o$33b2o2bobo2b2o12bo3bo3bo2b2obo4bo
2bobob2ob2obob2ob2o$32bo4bobo4bo11bo2b4obo7bo2b2obob2obo2bobo4b2o$33bo
bobobobobo12bob2o4bo2bo4bo3b3ob2o8b5o$59bob4ob6o2b2o2b2o6b2o4bo$56bo7b
2o8b2o2bo4bo7bo$55b5obo3b2o8bo5bo9bo$54b2ob2o19bobo$54b2o7b3obo$62b2o
2b3o$54b2o5bo2b2o3bo$54bob3o6bo3bo$53bobo15bo$64bo3bo2bo$54b2ob2obo3b
3o2bo$54b2obob2o5b2o$53bobobo2bo16b3ob3o$31b2o20bo8b2obobo7b2o4bob3o6b
o$28b2ob2o26bob2o2b2o7bobobob2o3bob3ob2obo$28b2o3bo26bobo12b6o9b3ob2o$
24b3o2bo21bo13b3o5bo7bo2b2ob2obobo5bo$24b2o2b3o5b3o11bobo8b5o5b3o3b2ob
o11bo2bo2b2o$24b3o9b3o8b2obobob2o9bo4b2obob3o2bobobo9bo3bobo$25bo9bo3b
o7b2o2b2ob2o4b3o3bo2bo5b4o3bo2bo4b3obob2o2bobo$26bo2bo13b2o2bobo3b2obo
8b3o9bobo2b2o14bobob2o$25b2ob2o4bo5bo3b2o2b2o4b2o2b2obo2b3ob2o4bo2b3ob
5o3b4o4b4o$29b7obob4ob2o2b6o4b2o2bo2b2o14bob2obo2b3ob5o2b3o$28bobobo9b
ob2o4b3o3bobo3b3o4bo3b4o3bo3b4o3bob3o5b2ob3obo$54bo2bobob2o6bo2b2obob
3o6bobo15b3ob2o$61bob2o11b6o3bo15bo3bobo2bo$57bob4o2b3o2b3o4b3o4bo16bo
3bo3bo$56bo2b2obo7bo34bo$55b2o8b3o2bo32bo$62b2o2b2o3bo32b2o$60b2obobo
3bo$60b5obo5bo$57bo7b3o3b3o$55b4o7bo7b2o$51b2ob2o3bo14b2o$51b2o2bo4b2o
b2ob3o5b2o4b2o$50bo2bo6bo4b3o9b2ob2o$66bo10b2o3bo$65b3o9b2o2$64b2ob2o
2$65b3o$65b3o$65b3o3$64b2ob2o$64b2ob2o$65b3o$66bo$65b3o2$64b2ob2o2$65b
3o$65b3o$65b3o3$64b2ob2o$64b2ob2o$65b3o$66bo$65b3o2$64b2ob2o2$65b3o$
65b3o$65b3o3$64b2ob2o$64b2ob2o$65b3o$66bo$65b3o2$64b2ob2o2$65b3o$65b3o
$65b3o3$64b2ob2o$64b2ob2o$65b3o$66bo$65b3o2$64b2ob2o2$65b3o$65b3o$65b
3o3$64b2ob2o$64b2ob2o$65b3o$66bo$65b3o2$64b2ob2o2$65b3o$65b3o$65b3o3$
64b2ob2o$64b2ob2o$65b3o$66bo$65b3o2$64b2ob2o2$65b3o$65b3o$65b3o3$64b2o
b2o$64b2ob2o$65b3o$66bo$65b3o2$64b2ob2o2$65b3o$65b3o$65b3o3$64b2ob2o$
64b2ob2o$65b3o$65b3o$65b3o$60b3o3bo3b3o$58b2obo9bob2o$58b3o3b5o3b3o$
59b2o4b3o4b2o$60bo11bo$63bo5bo2$60bobo7bobo$59b2o11b2o2$58bo15bo$59bo
13bo!

This would have seemed impossible to solve just a few years ago, and yet for Keith Amling it wasn't even the most impressive c/3 ship found that week.

c/3 Against-the-Grain Greyship

On August 31, 2023 Keith Amling constructed the first c/3 grayship where the stripes are perpendicular to the direction of travel ("against-the-grain"). Such grayships were previously only known to travel at speed c/2 with period 4.

A c/3 against-the-grain greyship must have period at least 6, which is typically far too high to reliably search at. Fortunately in this case, Amling's amazing search tools and a neat trick by Hartmut Holzwart and Jason Summers allowed this to be completed almost entirely with period-3 components. In a moment I will endeavor to explain how this is accomplished in detail, with a bit of history thrown in, but first let's see the actual ship:

Code: Select all

#C A c/3 against-the-grain greyship
#C By Keith Amling, August 31, 2023
#C Using ideas and components by Hartmut Holzwart and Jason Summers
#C This is a significant reduction to Amling's original ship
#C https://conwaylife.com/forums/viewtopic.php?p=166141#p166141
#C https://conwaylife.com/forums/viewtopic.php?p=129400#p129400
x = 501, y = 463, rule = B3/S23
228b2o41b2o$225b2ob2o41b2ob2o$225b2o3bo39bo3b2o$221b3o2bo47bo2b3o$221b
2o2b3o45b3o2b2o$221b3o53b3o$222bo55bo$223bo2bo47bo2bo$222b2ob2o2bo41bo
2b2ob2o$226b2ob2o39b2ob2o$225bob2o2bo37bo2b2obo$229bobo37bobo$229b2o
39b2o$228b2o41b2o$226bo2bo41bo2bo$226bo47bo$225bo3bo41bo3bo$225bo3bo
41bo3bo$228bo43bo$225b2o3bo39bo3b2o$224bo3b4o37b4o3bo$225bo4b2o37b2o4b
o2$225b2o47b2o$226bo47bo$226bo47bo$224b2o49b2o$223b2ob2o45b2ob2o$222bo
55bo$226bo47bo2$223b3o49b3o$218b2ob2o55b2ob2o$218b2o4b2o49b2o4b2o$218b
3ob2o53b2ob3o$218b2o2b2o53b2o2b2o$219bo61bo2$222b3o51b3o$223bo53bo$
220b2o3b2o47b2o3b2o$220b2o3b2o47b2o3b2o$221b5o49b5o$223bo53bo$223bo53b
o$222b3o51b3o3$221bo3bo49bo3bo$220b3ob3o47b3ob3o$218b2o7b2o43b2o7b2o$
218b2o7b2o10b3o17b3o10b2o7b2o$221b2ob2o9bob2o3bo15bo3b2obo9b2ob2o$221b
o3bo8b3o3bobo15bobo3b3o8bo3bo$222bobo8bo3bo4b2o13b2o4bo3bo8bobo$220bob
obobo7bo7b3o11b3o7bo7bobobobo$219bo2bobo2bo12bobo15bobo12bo2bobo2bo$
218bo9bo10b2o19b2o10bo9bo$217bo2bo5bo2bo8bo3bo15bo3bo8bo2bo5bo2bo$217b
o3bo3bo3bo12bo15bo12bo3bo3bo3bo$185bo33bob2ob2obo11bob2o7bo7b2obo11bob
2ob2obo33bo$181b3ob3o29bo2bobobobo2bo9bo9bobo9bo9bo2bobobobo2bo29b3ob
3o$180bo6b2o28bo3b2ob2o3bo9b3o6bo3bo6b3o9bo3b2ob2o3bo28b2o6bo$181b2o3b
o2bo59b3o59bo2bo3b2o$191b3o22b2o11b2o5bobo23bobo5b2o11b2o22b3o$187bo2b
obo42b2obob2o5b2o3b2o5b2obob2o42bobo2bo$187bo2bobo2b2obo16bo15bo2bo3bo
bo2b3o3bobo3b3o2bobo3bo2bo15bo16bob2o2bobo2bo$186bobobo2b2o2b3o15bobo
11bobo8bob2obo3bobo3bob2obo8bobo11bobo15b3o2b2o2bobobo$169bo18bobobo3b
o3bo19b2o3b2o13bobo6bobo6bobo13b2o3b2o19bo3bo3bobobo18bo$165b3ob3o27bo
15b2obob2o3b2obob2o8bobo2bobobobobobo2bobo8b2obob2o3b2obob2o15bo27b3ob
3o$164bo6b2o21bo24bo2bobo2bo9b2obobo15bobob2o9bo2bobo2bo24bo21b2o6bo$
165b2o3bo2bo21b2o23b3ob3o10b2obo4b2o7b2o4bob2o10b3ob3o23b2o21bo2bo3b2o
$175b3o17b2o21b3o5b3o14b2o11b2o14b3o5b3o21b2o17b3o$171bo2bobo19bo6b2o
12bo2bo5bo2bo9b2o3bo4b3o4bo3b2o9bo2bo5bo2bo12b2o6bo19bobo2bo$171bo2bob
o2b2obo15bob2ob2o11b2obo7bob2o6b3o2bo6b3o6bo2b3o6b2obo7bob2o11b2ob2obo
15bob2o2bobo2bo$170bobobo2b2o2b3o14b2obo3bo10b2o3bo3bo3b2o11bo5bo3bo5b
o11b2o3bo3bo3b2o10bo3bob2o14b3o2b2o2bobobo$153bo18bobobo3bo3bo9b3obob
3o2bo12b2o7b2o8b2o2bob7ob7obo2b2o8b2o7b2o12bo2b3obob3o9bo3bo3bobobo18b
o$149b3ob3o27bo12bobo3bo3bo9b6o3b6o5b3o2b4obo7bob4o2b3o5b6o3b6o9bo3bo
3bobo12bo27b3ob3o$148bo6b2o21bo16bo2bobo3bobo8bo3bo7bo3bo5bob3o6bobobo
6b3obo5bo3bo7bo3bo8bobo3bobo2bo16bo21b2o6bo$149b2o3bo2bo21b2o17bobo18b
2o5b2o9bo2bo6b3ob3o6bo2bo9b2o5b2o18bobo17b2o21bo2bo3b2o$159b3o17b2o15b
o3b2o19bo3bo21bo5bo21bo3bo19b2o3bo15b2o17b3o$155bo2bobo19bo6b2o7bo3b2o
b2o11b2obobo3bobob2o7bo3b2o4bo3bo4b2o3bo7b2obobo3bobob2o11b2ob2o3bo7b
2o6bo19bobo2bo$155bo2bobo2b2obo15bob2ob2o9bob2obo12bo4b2ob2o4bo12bo13b
o12bo4b2ob2o4bo12bob2obo9b2ob2obo15bob2o2bobo2bo$154bobobo2b2o2b3o14b
2obo3bo13bobo13b3o3b3o12b2obob2obo3bob2obob2o12b3o3b3o13bobo13bo3bob2o
14b3o2b2o2bobobo$137bo18bobobo3bo3bo9b3obob3o2bo9b4o2b2o11bo2bo3bo2bo
9b2obobobo3bobo3bobobob2o9bo2bo3bo2bo11b2o2b4o9bo2b3obob3o9bo3bo3bobob
o18bo$133b3ob3o27bo12bobo3bo3bo7b3obo15bob2o3b2obo8bobo3bobo3bobo3bobo
3bobo8bob2o3b2obo15bob3o7bo3bo3bobo12bo27b3ob3o$132bo6b2o21bo16bo2bobo
3bobo6b2o6b2o10b2obo5bob2o8b3o2bo2b2o2bo2b2o2bo2b3o8b2obo5bob2o10b2o6b
2o6bobo3bobo2bo16bo21b2o6bo$133b2o3bo2bo21b2o17bobo13bo6b2o10bo11bo14b
o3bobobo3bo14bo11bo10b2o6bo13bobo17b2o21bo2bo3b2o$143b3o17b2o15bo3b2o
11b2o5bobo12bobo3bobo8b2o5b2o2b7o2b2o5b2o8bobo3bobo12bobo5b2o11b2o3bo
15b2o17b3o$139bo2bobo19bo6b2o7bo3b2ob2o14bo32b2o9bo5bo9b2o32bo14b2ob2o
3bo7b2o6bo19bobo2bo$139bo2bobo2b2obo15bob2ob2o9bob2obo9b2o4bo14bo2bo3b
o2bo8b3o9b3o9b3o8bo2bo3bo2bo14bo4b2o9bob2obo9b2ob2obo15bob2o2bobo2bo$
138bobobo2b2o2b3o14b2obo3bo13bobo7b2o4bo14bob2o3b2obo10b2o4b4obob4o4b
2o10bob2o3b2obo14bo4b2o7bobo13bo3bob2o14b3o2b2o2bobobo$121bo18bobobo3b
o3bo9b3obob3o2bo9b4o2b2o5bobo6b3o10b2o7b2o8b2obo2b3o2b2ob2o2b3o2bob2o
8b2o7b2o10b3o6bobo5b2o2b4o9bo2b3obob3o9bo3bo3bobobo18bo$117b3ob3o27bo
12bobo3bo3bo7b3obo8bo12bo7b4o2bobo2b4o4bo2bobob2o3bobobobo3b2obobo2bo
4b4o2bobo2b4o7bo12bo8bob3o7bo3bo3bobo12bo27b3ob3o$116bo6b2o21bo16bo2bo
bo3bobo6b2o6b2o4bo8b2obo7b2obobobobobobob2o3b2obobobo2bob2obob2obo2bob
obob2o3b2obobobobobobob2o7bob2o8bo4b2o6b2o6bobo3bobo2bo16bo21b2o6bo$
117b2o3bo2bo21b2o17bobo13bo6b2o4bo7bo10b2o3b2obobob2o3b2obobobobobob2o
bo5bob2obobobobobob2o3b2obobob2o3b2o10bo7bo4b2o6bo13bobo17b2o21bo2bo3b
2o$127b3o17b2o15bo3b2o11b2o5bobo6b3o6b2o6bo2b2obobobobob2o2bobobobobob
obo11bobobobobobobo2b2obobobobob2o2bo6b2o6b3o6bobo5b2o11b2o3bo15b2o17b
3o$123bo2bobo19bo6b2o7bo3b2ob2o14bo12bo3bo3bo5bobobobobobobobobobobobo
bobobobobo3bo3bobobobobobobobobobobobobobobobobo5bo3bo3bo12bo14b2ob2o
3bo7b2o6bo19bobo2bo$123bo2bobo2b2obo15bob2ob2o9bob2obo9b2o4bo8b2obo5bo
5b2obobobobobobobobobobobobobobobobobobo3bobobobobobobobobobobobobobob
obobobob2o5bo5bob2o8bo4b2o9bob2obo9b2ob2obo15bob2o2bobo2bo$122bobobo2b
2o2b3o14b2obo3bo13bobo7b2o4bo7bo12bo3bobobobobobobobobobobobobobobobob
obobo3bobobobobobobobobobobobobobobobobobobo3bo12bo7bo4b2o7bobo13bo3bo
b2o14b3o2b2o2bobobo$105bo18bobobo3bo3bo9b3obob3o2bo9b4o2b2o5bobo6b3o6b
2o5bo2b3obobobobobobobobobobobobobobobobobobob2ob2obobobobobobobobobob
obobobobobobobobob3o2bo5b2o6b3o6bobo5b2o2b4o9bo2b3obob3o9bo3bo3bobobo
18bo$101b3ob3o27bo12bobo3bo3bo7b3obo8bo12bo3bo3bo4b2obobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
2o4bo3bo3bo12bo8bob3o7bo3bo3bobo12bo27b3ob3o$100bo6b2o21bo16bo2bobo3bo
bo6b2o6b2o4bo8b2obo5bo5b2obobobobobobobobobobobobobobobobobobobobo2bob
3obo2bobobobobobobobobobobobobobobobobobobobob2o5bo5bob2o8bo4b2o6b2o6b
obo3bobo2bo16bo21b2o6bo$101b2o3bo2bo21b2o17bobo13bo6b2o4bo7bo12bo3bobo
bobobobobobobobobobobobobobobobobobobo11bobobobobobobobobobobobobobobo
bobobobobobo3bo12bo7bo4b2o6bo13bobo17b2o21bo2bo3b2o$111b3o17b2o15bo3b
2o11b2o5bobo6b3o6b2o5bo2b3obobobobobobobobobobobobobobobobobobobo2bob
11obo2bobobobobobobobobobobobobobobobobobobob3o2bo5b2o6b3o6bobo5b2o11b
2o3bo15b2o17b3o$107bo2bobo19bo6b2o7bo3b2ob2o14bo12bo3bo3bo4b2obobobobo
bobobobobobobobobobobobobobobobobo19bobobobobobobobobobobobobobobobobo
bobobobob2o4bo3bo3bo12bo14b2ob2o3bo7b2o6bo19bobo2bo$107bo2bobo2b2obo
15bob2ob2o9bob2obo9b2o4bo8b2obo5bo5b2obobobobobobobobobobobobobobobobo
bobobobo2bob19obo2bobobobobobobobobobobobobobobobobobobobob2o5bo5bob2o
8bo4b2o9bob2obo9b2ob2obo15bob2o2bobo2bo$106bobobo2b2o2b3o14b2obo3bo13b
obo7b2o4bo7bo12bo3bobobobobobobobobobobobobobobobobobobobobo27bobobobo
bobobobobobobobobobobobobobobobobo3bo12bo7bo4b2o7bobo13bo3bob2o14b3o2b
2o2bobobo$89bo18bobobo3bo3bo9b3obob3o2bo9b4o2b2o5bobo6b3o6b2o5bo2b3obo
bobobobobobobobobobobobobobobobobobo2bob27obo2bobobobobobobobobobobobo
bobobobobobobob3o2bo5b2o6b3o6bobo5b2o2b4o9bo2b3obob3o9bo3bo3bobobo18bo
$85b3ob3o27bo12bobo3bo3bo7b3obo8bo12bo3bo3bo4b2obobobobobobobobobobobo
bobobobobobobobobobo35bobobobobobobobobobobobobobobobobobobobobob2o4bo
3bo3bo12bo8bob3o7bo3bo3bobo12bo27b3ob3o$84bo6b2o21bo16bo2bobo3bobo6b2o
6b2o4bo8b2obo5bo5b2obobobobobobobobobobobobobobobobobobobobo2bob35obo
2bobobobobobobobobobobobobobobobobobobobob2o5bo5bob2o8bo4b2o6b2o6bobo
3bobo2bo16bo21b2o6bo$85b2o3bo2bo21b2o17bobo13bo6b2o4bo7bo12bo3bobobobo
bobobobobobobobobobobobobobobobobo43bobobobobobobobobobobobobobobobobo
bobobobo3bo12bo7bo4b2o6bo13bobo17b2o21bo2bo3b2o$95b3o17b2o15bo3b2o11b
2o5bobo6b3o6b2o5bo2b3obobobobobobobobobobobobobobobobobobobo2bob43obo
2bobobobobobobobobobobobobobobobobobobob3o2bo5b2o6b3o6bobo5b2o11b2o3bo
15b2o17b3o$91bo2bobo19bo6b2o7bo3b2ob2o14bo12bo3bo3bo4b2obobobobobobobo
bobobobobobobobobobobobobobo51bobobobobobobobobobobobobobobobobobobobo
bob2o4bo3bo3bo12bo14b2ob2o3bo7b2o6bo19bobo2bo$91bo2bobo2b2obo15bob2ob
2o9bob2obo9b2o4bo8b2obo5bo5b2obobobobobobobobobobobobobobobobobobobobo
2bob51obo2bobobobobobobobobobobobobobobobobobobobob2o5bo5bob2o8bo4b2o
9bob2obo9b2ob2obo15bob2o2bobo2bo$90bobobo2b2o2b3o14b2obo3bo13bobo7b2o
4bo7bo12bo3bobobobobobobobobobobobobobobobobobobobobo59bobobobobobobob
obobobobobobobobobobobobobo3bo12bo7bo4b2o7bobo13bo3bob2o14b3o2b2o2bobo
bo$73bo18bobobo3bo3bo9b3obob3o2bo9b4o2b2o5bobo6b3o6b2o5bo2b3obobobobob
obobobobobobobobobobobobobobo2bob59obo2bobobobobobobobobobobobobobobob
obobobob3o2bo5b2o6b3o6bobo5b2o2b4o9bo2b3obob3o9bo3bo3bobobo18bo$69b3ob
3o27bo12bobo3bo3bo7b3obo8bo12bo3bo3bo4b2obobobobobobobobobobobobobobob
obobobobobobo67bobobobobobobobobobobobobobobobobobobobobob2o4bo3bo3bo
12bo8bob3o7bo3bo3bobo12bo27b3ob3o$68bo6b2o21bo16bo2bobo3bobo6b2o6b2o4b
o8b2obo5bo5b2obobobobobobobobobobobobobobobobobobobobo2bob67obo2bobobo
bobobobobobobobobobobobobobobobobob2o5bo5bob2o8bo4b2o6b2o6bobo3bobo2bo
16bo21b2o6bo$69b2o3bo2bo21b2o17bobo13bo6b2o4bo7bo12bo3bobobobobobobobo
bobobobobobobobobobobobobo75bobobobobobobobobobobobobobobobobobobobobo
3bo12bo7bo4b2o6bo13bobo17b2o21bo2bo3b2o$79b3o17b2o15bo3b2o11b2o5bobo6b
3o6b2o5bo2b3obobobobobobobobobobobobobobobobobobobo2bob75obo2bobobobob
obobobobobobobobobobobobobobob3o2bo5b2o6b3o6bobo5b2o11b2o3bo15b2o17b3o
$75bo2bobo19bo6b2o7bo3b2ob2o14bo12bo3bo3bo4b2obobobobobobobobobobobobo
bobobobobobobobobo83bobobobobobobobobobobobobobobobobobobobobob2o4bo3b
o3bo12bo14b2ob2o3bo7b2o6bo19bobo2bo$75bo2bobo2b2obo15bob2ob2o9bob2obo
9b2o4bo8b2obo5bo5b2obobobobobobobobobobobobobobobobobobobobo2bob83obo
2bobobobobobobobobobobobobobobobobobobobob2o5bo5bob2o8bo4b2o9bob2obo9b
2ob2obo15bob2o2bobo2bo$74bobobo2b2o2b3o14b2obo3bo13bobo7b2o4bo7bo12bo
3bobobobobobobobobobobobobobobobobobobobobo91bobobobobobobobobobobobob
obobobobobobobobo3bo12bo7bo4b2o7bobo13bo3bob2o14b3o2b2o2bobobo$57bo18b
obobo3bo3bo9b3obob3o2bo9b4o2b2o5bobo6b3o6b2o5bo2b3obobobobobobobobobob
obobobobobobobobobo2bob91obo2bobobobobobobobobobobobobobobobobobobob3o
2bo5b2o6b3o6bobo5b2o2b4o9bo2b3obob3o9bo3bo3bobobo18bo$53b3ob3o27bo12bo
bo3bo3bo7b3obo8bo12bo3bo3bo4b2obobobobobobobobobobobobobobobobobobobob
obo99bobobobobobobobobobobobobobobobobobobobobob2o4bo3bo3bo12bo8bob3o
7bo3bo3bobo12bo27b3ob3o$52bo6b2o21bo16bo2bobo3bobo6b2o6b2o4bo8b2obo5bo
5b2obobobobobobobobobobobobobobobobobobobobo2bob99obo2bobobobobobobobo
bobobobobobobobobobobobob2o5bo5bob2o8bo4b2o6b2o6bobo3bobo2bo16bo21b2o
6bo$53b2o3bo2bo21b2o17bobo13bo6b2o4bo7bo12bo3bobobobobobobobobobobobob
obobobobobobobobo107bobobobobobobobobobobobobobobobobobobobobo3bo12bo
7bo4b2o6bo13bobo17b2o21bo2bo3b2o$63b3o17b2o15bo3b2o11b2o5bobo6b3o6b2o
5bo2b3obobobobobobobobobobobobobobobobobobobo2bob107obo2bobobobobobobo
bobobobobobobobobobobobob3o2bo5b2o6b3o6bobo5b2o11b2o3bo15b2o17b3o$59bo
2bobo19bo6b2o7bo3b2ob2o14bo12bo3bo3bo4b2obobobobobobobobobobobobobobob
obobobobobobo115bobobobobobobobobobobobobobobobobobobobobob2o4bo3bo3bo
12bo14b2ob2o3bo7b2o6bo19bobo2bo$59bo2bobo2b2obo15bob2ob2o9bob2obo9b2o
4bo8b2obo5bo5b2obobobobobobobobobobobobobobobobobobobobo2bob115obo2bob
obobobobobobobobobobobobobobobobobobob2o5bo5bob2o8bo4b2o9bob2obo9b2ob
2obo15bob2o2bobo2bo$58bobobo2b2o2b3o14b2obo3bo13bobo7b2o4bo7bo12bo3bob
obobobobobobobobobobobobobobobobobobobo123bobobobobobobobobobobobobobo
bobobobobobobo3bo12bo7bo4b2o7bobo13bo3bob2o14b3o2b2o2bobobo$60bobobo3b
o3bo9b3obob3o2bo9b4o2b2o5bobo6b3o6b2o5bo2b3obobobobobobobobobobobobobo
bobobobobobo2bob123obo2bobobobobobobobobobobobobobobobobobobob3o2bo5b
2o6b3o6bobo5b2o2b4o9bo2b3obob3o9bo3bo3bobobo$71bo12bobo3bo3bo7b3obo8bo
12bo3bo3bo4b2obobobobobobobobobobobobobobobobobobobobobo131bobobobobob
obobobobobobobobobobobobobobobob2o4bo3bo3bo12bo8bob3o7bo3bo3bobo12bo$
66bo16bo2bobo3bobo6b2o6b2o4bo8b2obo5bo5b2obobobobobobobobobobobobobobo
bobobobobobo2bob131obo2bobobobobobobobobobobobobobobobobobobobob2o5bo
5bob2o8bo4b2o6b2o6bobo3bobo2bo16bo$67b2o17bobo13bo6b2o4bo7bo12bo3bobob
obobobobobobobobobobobobobobobobobobo139bobobobobobobobobobobobobobobo
bobobobobobo3bo12bo7bo4b2o6bo13bobo17b2o$67b2o15bo3b2o11b2o5bobo6b3o6b
2o5bo2b3obobobobobobobobobobobobobobobobobobobo2bob139obo2bobobobobobo
bobobobobobobobobobobobobob3o2bo5b2o6b3o6bobo5b2o11b2o3bo15b2o$68bo6b
2o7bo3b2ob2o14bo12bo3bo3bo4b2obobobobobobobobobobobobobobobobobobobobo
bo147bobobobobobobobobobobobobobobobobobobobobob2o4bo3bo3bo12bo14b2ob
2o3bo7b2o6bo$70bob2ob2o9bob2obo9b2o4bo8b2obo5bo5b2obobobobobobobobobob
obobobobobobobobobobo2bob147obo2bobobobobobobobobobobobobobobobobobobo
bob2o5bo5bob2o8bo4b2o9bob2obo9b2ob2obo$70b2obo3bo13bobo7b2o4bo7bo12bo
3bobobobobobobobobobobobobobobobobobobobobo155bobobobobobobobobobobobo
bobobobobobobobobo3bo12bo7bo4b2o7bobo13bo3bob2o$66b3obob3o2bo9b4o2b2o
5bobo6b3o6b2o5bo2b3obobobobobobobobobobobobobobobobobobobo2bob155obo2b
obobobobobobobobobobobobobobobobobobob3o2bo5b2o6b3o6bobo5b2o2b4o9bo2b
3obob3o$68bobo3bo3bo7b3obo8bo12bo3bo3bo4b2obobobobobobobobobobobobobob
obobobobobobobo163bobobobobobobobobobobobobobobobobobobobobob2o4bo3bo
3bo12bo8bob3o7bo3bo3bobo$67bo2bobo3bobo6b2o6b2o4bo8b2obo5bo5b2obobobob
obobobobobobobobobobobobobobobobo2bob163obo2bobobobobobobobobobobobobo
bobobobobobobob2o5bo5bob2o8bo4b2o6b2o6bobo3bobo2bo$70bobo13bo6b2o4bo7b
o12bo3bobobobobobobobobobobobobobobobobobobobobo171bobobobobobobobobob
obobobobobobobobobobobo3bo12bo7bo4b2o6bo13bobo$68bo3b2o11b2o5bobo6b3o
6b2o5bo2b3obobobobobobobobobobobobobobobobobobobo2bob171obo2bobobobobo
bobobobobobobobobobobobobobob3o2bo5b2o6b3o6bobo5b2o11b2o3bo$68bo3b2ob
2o14bo12bo3bo3bo4b2obobobobobobobobobobobobobobobobobobobobobo179bobob
obobobobobobobobobobobobobobobobobobob2o4bo3bo3bo12bo14b2ob2o3bo$70bob
2obo9b2o4bo8b2obo5bo5b2obobobobobobobobobobobobobobobobobobobobo2bob
179obo2bobobobobobobobobobobobobobobobobobobobob2o5bo5bob2o8bo4b2o9bob
2obo$75bobo7b2o4bo7bo12bo3bobobobobobobobobobobobobobobobobobobobobo
187bobobobobobobobobobobobobobobobobobobobobo3bo12bo7bo4b2o7bobo$71b4o
2b2o5bobo6b3o6b2o5bo2b3obobobobobobobobobobobobobobobobobobobo2bob187o
bo2bobobobobobobobobobobobobobobobobobobob3o2bo5b2o6b3o6bobo5b2o2b4o$
70b3obo8bo12bo3bo3bo4b2obobobobobobobobobobobobobobobobobobobobobo195b
obobobobobobobobobobobobobobobobobobobobob2o4bo3bo3bo12bo8bob3o$69b2o
6b2o4bo8b2obo5bo5b2obobobobobobobobobobobobobobobobobobobobo2bob195obo
2bobobobobobobobobobobobobobobobobobobobob2o5bo5bob2o8bo4b2o6b2o$70bo
6b2o4bo7bo12bo3bobobobobobobobobobobobobobobobobobobobobo203bobobobobo
bobobobobobobobobobobobobobobobo3bo12bo7bo4b2o6bo$69b2o5bobo6b3o6b2o5b
o2b3obobobobobobobobobobobobobobobobobobobo2bob203obo2bobobobobobobobo
bobobobobobobobobobobob3o2bo5b2o6b3o6bobo5b2o$75bo12bo3bo3bo4b2obobobo
bobobobobobobobobobobobobobobobobobo211bobobobobobobobobobobobobobobob
obobobobobob2o4bo3bo3bo12bo$69b2o4bo8b2obo5bo5b2obobobobobobobobobobob
obobobobobobobobobo2bob211obo2bobobobobobobobobobobobobobobobobobobobo
b2o5bo5bob2o8bo4b2o$69b2o4bo7bo12bo3bobobobobobobobobobobobobobobobobo
bobobobo219bobobobobobobobobobobobobobobobobobobobobo3bo12bo7bo4b2o$
68bobo6b3o6b2o5bo2b3obobobobobobobobobobobobobobobobobobobo2bob219obo
2bobobobobobobobobobobobobobobobobobobob3o2bo5b2o6b3o6bobo$67bo12bo3bo
3bo4b2obobobobobobobobobobobobobobobobobobobobobo227bobobobobobobobobo
bobobobobobobobobobobobob2o4bo3bo3bo12bo$67bo8b2obo5bo5b2obobobobobobo
bobobobobobobobobobobobobobo2bob227obo2bobobobobobobobobobobobobobobob
obobobobob2o5bo5bob2o8bo$67bo7bo12bo3bobobobobobobobobobobobobobobobob
obobobobo235bobobobobobobobobobobobobobobobobobobobobo3bo12bo7bo$69b3o
6b2o5bo2b3obobobobobobobobobobobobobobobobobobobo2bob235obo2bobobobobo
bobobobobobobobobobobobobobob3o2bo5b2o6b3o$72bo3bo3bo4b2obobobobobobob
obobobobobobobobobobobobobobo243bobobobobobobobobobobobobobobobobobobo
bobob2o4bo3bo3bo$68b2obo5bo5b2obobobobobobobobobobobobobobobobobobobob
o2bob243obo2bobobobobobobobobobobobobobobobobobobobob2o5bo5bob2o$41b2o
b3o8b3ob2o6bo12bo3bobobobobobobobobobobobobobobobobobobobobo251bobobob
obobobobobobobobobobobobobobobobobo3bo12bo6b2ob3o8b3ob2o$41b2o4b2o4b2o
4b2o9b2o5bo2b3obobobobobobobobobobobobobobobobobobobo2bob251obo2bobobo
bobobobobobobobobobobobobobobobob3o2bo5b2o9b2o4b2o4b2o4b2o$40bo2bobo3b
o2bobob3o9bo3bo4b2obobobobobobobobobobobobobobobobobobobobobo259bobobo
bobobobobobobobobobobobobobobobobobob2o4bo3bo9b3obobo2bo3bobo2bo$47b3o
2bob2ob2o2b2o6bo5b2obobobobobobobobobobobobobobobobobobobobo2bob259obo
2bobobobobobobobobobobobobobobobobobobobob2o5bo6b2o2b2ob2obo2b3o$49b2o
8bob3obo6bo3bobobobobobobobobobobobobobobobobobobobobo267bobobobobobob
obobobobobobobobobobobobobobo3bo6bob3obo8b2o$49bo4bobo4bob4o2bo2b3obob
obobobobobobobobobobobobobobobobobo2bob267obo2bobobobobobobobobobobobo
bobobobobobobob3o2bo2b4obo4bobo4bo$50b2o2b3o2bo6bo2b2obobobobobobobobo
bobobobobobobobobobobobobo275bobobobobobobobobobobobobobobobobobobobob
ob2o2bo6bo2b3o2b2o$52b3ob3o3bo3bobobobobobobobobobobobobobobobobobobob
obobo2bob275obo2bobobobobobobobobobobobobobobobobobobobobobo3bo3b3ob3o
$53b2obo5bo3bobobobobobobobobobobobobobobobobobobobobobo283bobobobobob
obobobobobobobobobobobobobobobobo3bo5bob2o$51bo4bo11bobobobobobobobobo
bobobobobobobobobobo2bob283obo2bobobobobobobobobobobobobobobobobobobo
11bo4bo$52bobo10b2obobobobobobobobobobobobobobobobobobobo291bobobobobo
bobobobobobobobobobobobobobob2o10bobo$65b2obobobobobobobobobobobobobob
obobobo2bob291obo2bobobobobobobobobobobobobobobobobob2o$17bo12bo35bobo
bobobobobobobobobobobobobobobobo299bobobobobobobobobobobobobobobobobob
o35bo12bo$9b2o4b4o9b4o6bo6bo21b2obobobobobobobobobobobobobobo2bob299ob
o2bobobobobobobobobobobobobobob2o21bo6bo6b4o9b4o4b2o$8b2o4b2o3bo7b2o3b
o4bobo4b4o18b3obobobobobobobobobobobobobobo307bobobobobobobobobobobobo
bobob3o18b4o4bobo4bo3b2o7bo3b2o4b2o$8b2ob2o4bobo5bo2bo3bo3bo3bo2bo3b2o
11b3o4b4obobobobobobobobobobobo2bob307obo2bobobobobobobobobobobob4o4b
3o11b2o3bo2bo3bo3bo3bo2bo5bobo4b2ob2o$5bob2o2bobob4o5bo2bo6bo8bo5bo8b
2obo8bobobobobobobobobobobobo315bobobobobobobobobobobobo8bob2o8bo5bo8b
o6bo2bo5b4obobo2b2obo$b3ob2o4bo4b2o6bo7bo2b2o2bobobob2obobo4bobo3bob2o
5bobobobobobobobobobo2bob315obo2bobobobobobobobobobo5b2obo3bobo4bobob
2obobobo2b2o2bo7bo6b2o4bo4b2ob3o$o6bob5obo3bo6bo7bob2obo5b2o4b2obob5o
2bobobo2bobobobobobobobobobo323bobobobobobobobobobo2bobobo2b5obob2o4b
2o5bob2obo7bo6bo3bob5obo6bo$b2o3bo4bo2bo4b2o3bo5b2ob2o6bobo3b2o2b2o5b
2o2bo2b2obobobobobobobobobo2bob323obo2bobobobobobobobobob2o2bo2b2o5b2o
2b2o3bobo6b2ob2o5bo3b2o4bo2bo4bo3b2o$22bobobo3bob2obob3o4bob3o3bobob2o
4b2obo2bobobobobobobobobo331bobobobobobobobobo2bob2o4b2obobo3b3obo4b3o
bob2obo3bobobo$19bo3bo3b2o8bobobo2bobo2bo15bob2obobobobobobo2bob331obo
2bobobobobobob2obo15bo2bobo2bobobo8b2o3bo3bo$23bobob2o3b2obo3bob2obo3b
5o12b2o3bobobobobobo339bobobobobobo3b2o12b5o3bob2obo3bob2o3b2obobo$18b
5o2bo3b2ob2o5b2obo5bo2bo17b2obobobo2bob339obo2bobobob2o17bo2bo5bob2o5b
2ob2o3bo2b5o$17b2o5bo8b4obobobobo8b3o3b4o7bobobobo347bobobobo7b4o3b3o
8bobobobob4o8bo5b2o$24bo4bo2bobobo2bo2bob2ob2o2b2o4b3ob2o3b3obobo2bob
347obo2bobob3o3b2ob3o4b2o2b2ob2obo2bo2bobobo2bo4bo$21b5o2b2obo2b3o2bo
2bo4b5ob2o2bo6b3obobobo355bobobob3o6bo2b2ob5o4bo2bo2b3o2bob2o2b5o$19bo
3bo4b2o5bobo8b2o2b2o3bo2b2o2bobo3bo2bob355obo2bo3bobo2b2o2bo3b2o2b2o8b
obo5b2o4bo3bo$17b3o8b2o2bobo10b2o8b2o5bobobo367bobobo5b2o8b2o10bobo2b
2o8b3o$13b2ob2o3bo5bo18bo3bo3b3o2b2obo6b363o6bob2o2b3o3bo3bo18bo5bo3b
2ob2o$13b2o2bo2bo5b2o17b2o4bo4bobobobo2bobo365bobo2bobobobo4bo4b2o17b
2o5bo2bo2b2o$12bo2bo41b2obobo4b367o4bobob2o41bo2bo$56b2o2bo4bobo365bob
o4bo2b2o$33b3ob2obo9b2o4b3o4b2o4bob359obo4b2o4b3o4b2o9bob2ob3o$29bob2o
4b2ob2o8b2ob2o7bo3b2obo361bob2o3bo7b2ob2o8b2ob2o4b2obo$28b3o3bo3b2o2bo
7b2o2bo2bo4bobob2obo2b357o2bob2obobo4bo2bo2b2o7bo2b2o3bo3b3o$27bo3bo4b
o17b2obo2bo3bo2bobobo357bobobo2bo3bo2bob2o17bo4bo3bo$28bo8bo5b2o3b2o2b
6o2bo6bobobob355obobobo6bo2b6o2b2o3b2o5bo8bo$36b2o2bo2bob5o2b2o3b3o5bo
bobobo357bobobobo5b3o3b2o2b5obo2bo2b2o$40b2obo2bo14b2ob2obobobobob351o
bobobobob2ob2o14bo2bob2o$43bob5o9b2o3b2obobobobo353bobobobob2o3b2o9b5o
bo$40b2obobobo2bo6b3o2bo2b3obobobo2b349o2bobobob3o2bo2b3o6bo2bobobob2o
$47b2obo2b3ob2ob2ob3obobobobobo349bobobobobob3ob2ob2ob3o2bob2o$46b2o2b
obo7bo6bobobobobob347obobobobobo6bo7bobo2b2o$44bo4bo4b2obobo6bo2bobobo
bo349bobobobo2bo6bobob2o4bo4bo$43b2obo2bob2o13b2obobobobobob343obobobo
bobob2o13b2obo2bob2o$42bo2bo2b2o19bobobobobo345bobobobobo19b2o2bo2bo$
43bo4b2o19bobobobobo2b341o2bobobobobo19b2o4bo$59b3o5bobobobobobobo341b
obobobobobobo5b3o$58bo7b3o2bobobobobob339obobobobobo2b3o7bo$56b3o4bo2b
o2b2o2bobobobo341bobobobo2b2o2bo2bo4b3o$52b3obobob5obo5bo2bobobobob
335obobobobo2bo5bob5obobob3o$51bo9bo2bobo4b2o2bobobobo337bobobobo2b2o
4bobo2bo9bo$52bo2bo10bob4o3bobobobo2b333o2bobobobo3b4obo10bo2bo$56bo9b
o4bo2b2obobobobo333bobobobob2o2bo4bo9bo$54b2o11bo6b2obobobobob331obobo
bobob2o6bo11b2o$69b2o5bo2bobobo333bobobo2bo5b2o$74bo2bobobobobob327obo
bobobobo2bo$75bo5bobobo329bobobo5bo$81bobobo2b325o2bobobo$81bobobobo
325bobobobo$78b2obobobobob323obobobobob2o$78b2obobobobo325bobobobob2o$
81bobobobobob319obobobobobo$80bo2bobobobo321bobobobo2bo$78b3o2bobobobo
2b317o2bobobobo2b3o$82b2obobobobo317bobobobob2o$85bobobobob315obobobob
o$81bo3bobobobo317bobobobo3bo$81bo2b3o2bobobob311obobobo2b3o2bo$82bo3b
2obobobo313bobobob2o3bo$89bobobo2b309o2bobobo$86b2obobobobo309bobobobo
b2o$85bo3bobobobob307obobobobo3bo$85bo2bo2bobobo309bobobo2bo2bo$84b2o
2bo2bobobobob303obobobobo2bo2b2o$83bob2o2bobobobobo305bobobobobo2b2obo
$82bo3bob3o2bobobo2b301o2bobobo2b3obo3bo$82bo7bob2obobobo301bobobob2ob
o7bo$85bo2bob2obobobobob299obobobobob2obo2bo$82b2o9bobobobo301bobobobo
9b2o$81bo13bobobobob295obobobobo13bo$81b2o7bobobo2bobobo297bobobo2bobo
bo7b2o$82b3o5bo6bobobo2b293o2bobobo6bo5b3o$82bo2bo3bobo5bobobobo293bob
obobo5bobo3bo2bo$86bo4bo2b2obobobobob291obobobobob2o2bo4bo$94b2obobobo
bo293bobobobob2o$81b2obobo10bobobobobob287obobobobobo10bobob2o$81b2o3b
o9bo2bobobobo289bobobobo2bo9bo3b2o$80bo2bo10b3o2bobobobo2b285o2bobobob
o2b3o10bo2bo$86b5o7b2obobobobo285bobobobob2o7b5o$85bobob2o10bobobobob
283obobobobo10b2obobo$84b2o4bo6bo3bobobobo285bobobobo3bo6bo4b2o$84b3o
3b2o5bo2b3o2bobobob279obobobo2b3o2bo5b2o3b3o$83bo3bobo2bo5bo3b2obobobo
281bobobob2o3bo5bo2bobo3bo$82bo2bob5o13bobobo2b277o2bobobo13b5obo2bo$
84bo4bob2o9b2obobobobo277bobobobob2o9b2obo4bo$81b4obob2o2b2o7bo3bobobo
bob275obobobobo3bo7b2o2b2obob4o$80b2o8bo10bo2bo2bobobo277bobobo2bo2bo
10bo8b2o$100b2o2bo2bobobobob271obobobobo2bo2b2o$91b2o6bob2o2bobobobobo
273bobobobobo2b2obo6b2o$87b3ob2o5bo3bob3o2bobobo2b269o2bobobo2b3obo3bo
5b2ob3o$83bob2obo9bo7bob2obobobo269bobobob2obo7bo9bob2obo$82b3o4bo11bo
2bob2obobobobob267obobobobob2obo2bo11bo4b3o$81bo3bo12b2o9bobobobo269bo
bobobo9b2o12bo3bo$82bo14bo13bobobobob263obobobobo13bo14bo$97b2o7bobobo
2bobobo265bobobo2bobobo7b2o$98b3o5bo6bobobo2b261o2bobobo6bo5b3o$98bo2b
o3bobo5bobobobo261bobobobo5bobo3bo2bo$102bo4bo2b2obobobobob259obobobob
ob2o2bo4bo$110b2obobobobo261bobobobob2o$97b2obobo10bobobobobob255obobo
bobobo10bobob2o$97b2o3bo9bo2bobobobo257bobobobo2bo9bo3b2o$96bo2bo10b3o
2bobobobo2b253o2bobobobo2b3o10bo2bo$102b5o7b2obobobobo253bobobobob2o7b
5o$101bobob2o10bobobobob251obobobobo10b2obobo$100b2o4bo6bo3bobobobo
253bobobobo3bo6bo4b2o$100b3o3b2o5bo2b3o2bobobob247obobobo2b3o2bo5b2o3b
3o$99bo3bobo2bo5bo3b2obobobo249bobobob2o3bo5bo2bobo3bo$98bo2bob5o13bob
obo2b245o2bobobo13b5obo2bo$100bo4bob2o9b2obobobobo245bobobobob2o9b2obo
4bo$97b4obob2o2b2o7bo3bobobobob243obobobobo3bo7b2o2b2obob4o$96b2o8bo
10bo2bo2bobobo245bobobo2bo2bo10bo8b2o$116b2o2bo2bobobobob239obobobobo
2bo2b2o$107b2o6bob2o2bobobobobo241bobobobobo2b2obo6b2o$103b3ob2o5bo3bo
b3o2bobobo2b237o2bobobo2b3obo3bo5b2ob3o$99bob2obo9bo7bob2obobobo237bob
obob2obo7bo9bob2obo$98b3o4bo11bo2bob2obobobobob235obobobobob2obo2bo11b
o4b3o$97bo3bo12b2o9bobobobo237bobobobo9b2o12bo3bo$98bo14bo13bobobobob
231obobobobo13bo14bo$113b2o7bobobo2bobobo233bobobo2bobobo7b2o$114b3o5b
o6bobobo2b229o2bobobo6bo5b3o$114bo2bo3bobo5bobobobo229bobobobo5bobo3bo
2bo$118bo4bo2b2obobobobob227obobobobob2o2bo4bo$126b2obobobobo229bobobo
bob2o$113b2obobo10bobobobobob223obobobobobo10bobob2o$113b2o3bo9bo2bobo
bobo225bobobobo2bo9bo3b2o$112bo2bo10b3o2bobobobo2b221o2bobobobo2b3o10b
o2bo$118b5o7b2obobobobo221bobobobob2o7b5o$117bobob2o10bobobobob219obob
obobo10b2obobo$116b2o4bo6bo3bobobobo221bobobobo3bo6bo4b2o$116b3o3b2o5b
o2b3o2bobobob215obobobo2b3o2bo5b2o3b3o$115bo3bobo2bo5bo3b2obobobo217bo
bobob2o3bo5bo2bobo3bo$114bo2bob5o13bobobo2b213o2bobobo13b5obo2bo$116bo
4bob2o9b2obobobobo213bobobobob2o9b2obo4bo$113b4obob2o2b2o7bo3bobobobob
211obobobobo3bo7b2o2b2obob4o$112b2o8bo10bo2bo2bobobo213bobobo2bo2bo10b
o8b2o$132b2o2bo2bobobobob207obobobobo2bo2b2o$123b2o6bob2o2bobobobobo
209bobobobobo2b2obo6b2o$119b3ob2o5bo3bob3o2bobobo2b205o2bobobo2b3obo3b
o5b2ob3o$115bob2obo9bo7bob2obobobo205bobobob2obo7bo9bob2obo$114b3o4bo
11bo2bob2obobobobob203obobobobob2obo2bo11bo4b3o$113bo3bo12b2o9bobobobo
205bobobobo9b2o12bo3bo$114bo14bo13bobobobob199obobobobo13bo14bo$129b2o
7bobobo2bobobo201bobobo2bobobo7b2o$130b3o5bo6bobobo2b197o2bobobo6bo5b
3o$130bo2bo3bobo5bobobobo197bobobobo5bobo3bo2bo$134bo4bo2b2obobobobob
195obobobobob2o2bo4bo$142b2obobobobo197bobobobob2o$129b2obobo10bobobob
obob191obobobobobo10bobob2o$129b2o3bo9bo2bobobobo193bobobobo2bo9bo3b2o
$128bo2bo10b3o2bobobobo2b189o2bobobobo2b3o10bo2bo$134b5o7b2obobobobo
189bobobobob2o7b5o$133bobob2o10bobobobob187obobobobo10b2obobo$132b2o4b
o6bo3bobobobo189bobobobo3bo6bo4b2o$132b3o3b2o5bo2b3o2bobobob183obobobo
2b3o2bo5b2o3b3o$131bo3bobo2bo5bo3b2obobobo185bobobob2o3bo5bo2bobo3bo$
130bo2bob5o13bobobo2b181o2bobobo13b5obo2bo$132bo4bob2o9b2obobobobo181b
obobobob2o9b2obo4bo$129b4obob2o2b2o7bo3bobobobob179obobobobo3bo7b2o2b
2obob4o$128b2o8bo10bo2bo2bobobo181bobobo2bo2bo10bo8b2o$148b2o2bo2bobob
obob175obobobobo2bo2b2o$139b2o6bob2o2bobobobobo177bobobobobo2b2obo6b2o
$135b3ob2o5bo3bob3o2bobobo2b173o2bobobo2b3obo3bo5b2ob3o$131bob2obo9bo
7bob2obobobo173bobobob2obo7bo9bob2obo$130b3o4bo11bo2bob2obobobobob171o
bobobobob2obo2bo11bo4b3o$129bo3bo12b2o9bobobobo173bobobobo9b2o12bo3bo$
130bo14bo13bobobobob167obobobobo13bo14bo$145b2o7bobobo2bobobo169bobobo
2bobobo7b2o$146b3o5bo6bobobo2b165o2bobobo6bo5b3o$146bo2bo3bobo5bobobob
o165bobobobo5bobo3bo2bo$150bo4bo2b2obobobobob163obobobobob2o2bo4bo$
158b2obobobobo165bobobobob2o$145b2obobo10bobobobobob159obobobobobo10bo
bob2o$145b2o3bo9bo2bobobobo161bobobobo2bo9bo3b2o$144bo2bo10b3o2bobobob
o2b157o2bobobobo2b3o10bo2bo$150b5o7b2obobobobo157bobobobob2o7b5o$149bo
bob2o10bobobobob155obobobobo10b2obobo$148b2o4bo6bo3bobobobo157bobobobo
3bo6bo4b2o$148b3o3b2o5bo2b3o2bobobob151obobobo2b3o2bo5b2o3b3o$147bo3bo
bo2bo5bo3b2obobobo153bobobob2o3bo5bo2bobo3bo$146bo2bob5o13bobobo2b149o
2bobobo13b5obo2bo$148bo4bob2o9b2obobobobo149bobobobob2o9b2obo4bo$145b
4obob2o2b2o7bo3bobobobob147obobobobo3bo7b2o2b2obob4o$144b2o8bo10bo2bo
2bobobo149bobobo2bo2bo10bo8b2o$164b2o2bo2bobobobob143obobobobo2bo2b2o$
155b2o6bob2o2bobobobobo145bobobobobo2b2obo6b2o$151b3ob2o5bo3bob3o2bobo
bo2b141o2bobobo2b3obo3bo5b2ob3o$147bob2obo9bo7bob2obobobo141bobobob2ob
o7bo9bob2obo$146b3o4bo11bo2bob2obobobobob139obobobobob2obo2bo11bo4b3o$
145bo3bo12b2o9bobobobo141bobobobo9b2o12bo3bo$146bo14bo13bobobobob135ob
obobobo13bo14bo$161b2o7bobobo2bobobo137bobobo2bobobo7b2o$162b3o5bo6bob
obo2b133o2bobobo6bo5b3o$162bo2bo3bobo5bobobobo133bobobobo5bobo3bo2bo$
166bo4bo2b2obobobobob131obobobobob2o2bo4bo$174b2obobobobo133bobobobob
2o$161b2obobo10bobobobobob127obobobobobo10bobob2o$161b2o3bo9bo2bobobob
o129bobobobo2bo9bo3b2o$160bo2bo10b3o2bobobobo2b125o2bobobobo2b3o10bo2b
o$166b5o7b2obobobobo125bobobobob2o7b5o$165bobob2o10bobobobob123obobobo
bo10b2obobo$164b2o4bo6bo3bobobobo125bobobobo3bo6bo4b2o$164b3o3b2o5bo2b
3o2bobobob119obobobo2b3o2bo5b2o3b3o$163bo3bobo2bo5bo3b2obobobo121bobob
ob2o3bo5bo2bobo3bo$162bo2bob5o13bobobo2b117o2bobobo13b5obo2bo$164bo4bo
b2o9b2obobobobo117bobobobob2o9b2obo4bo$161b4obob2o2b2o7bo3bobobobob
115obobobobo3bo7b2o2b2obob4o$160b2o8bo10bo2bo2bobobo117bobobo2bo2bo10b
o8b2o$180b2o2bo2bobobobob111obobobobo2bo2b2o$171b2o6bob2o2bobobobobo
113bobobobobo2b2obo6b2o$167b3ob2o5bo3bob3o2bobobo2b109o2bobobo2b3obo3b
o5b2ob3o$163bob2obo9bo7bob2obobobo109bobobob2obo7bo9bob2obo$162b3o4bo
11bo2bob2obobobobob107obobobobob2obo2bo11bo4b3o$161bo3bo12b2o9bobobobo
109bobobobo9b2o12bo3bo$162bo14bo13bobobobob103obobobobo13bo14bo$177b2o
7bobobo2bobobo105bobobo2bobobo7b2o$178b3o5bo6bobobo2b101o2bobobo6bo5b
3o$178bo2bo3bobo5bobobobo101bobobobo5bobo3bo2bo$182bo4bo2b2obobobobob
99obobobobob2o2bo4bo$190b2obobobobo101bobobobob2o$177b2obobo10bobobobo
bob95obobobobobo10bobob2o$177b2o3bo9bo2bobobobo97bobobobo2bo9bo3b2o$
176bo2bo10b3o2bobobobo2b93o2bobobobo2b3o10bo2bo$182b5o7b2obobobobo93bo
bobobob2o7b5o$181bobob2o10bobobobob91obobobobo10b2obobo$180b2o4bo6bo3b
obobobo93bobobobo3bo6bo4b2o$180b3o3b2o5bo2b3o2bobobob87obobobo2b3o2bo
5b2o3b3o$179bo3bobo2bo5bo3b2obobobo89bobobob2o3bo5bo2bobo3bo$178bo2bob
5o13bobobo2b85o2bobobo13b5obo2bo$180bo4bob2o9b2obobobobo85bobobobob2o
9b2obo4bo$177b4obob2o2b2o7bo3bobobobob83obobobobo3bo7b2o2b2obob4o$176b
2o8bo10bo2bo2bobobo85bobobo2bo2bo10bo8b2o$196b2o2bo2bobobobob79obobobo
bo2bo2b2o$187b2o6bob2o2bobobobobo81bobobobobo2b2obo6b2o$183b3ob2o5bo3b
ob3o2bobobo2b77o2bobobo2b3obo3bo5b2ob3o$179bob2obo9bo7bob2obobobo77bob
obob2obo7bo9bob2obo$178b3o4bo11bo2bob2obobobobob75obobobobob2obo2bo11b
o4b3o$177bo3bo12b2o9bobobobo77bobobobo9b2o12bo3bo$178bo14bo13bobobobob
71obobobobo13bo14bo$193b2o7bobobo2bobobo73bobobo2bobobo7b2o$194b3o5bo
6bobobo2b69o2bobobo6bo5b3o$194bo2bo3bobo5bobobobo69bobobobo5bobo3bo2bo
$198bo4bo2b2obobobobob67obobobobob2o2bo4bo$206b2obobobobo69bobobobob2o
$193b2obobo10bobobobobob63obobobobobo10bobob2o$193b2o3bo9bo2bobobobo
65bobobobo2bo9bo3b2o$192bo2bo10b3o2bobobobo2b61o2bobobobo2b3o10bo2bo$
198b5o7b2obobobobo61bobobobob2o7b5o$197bobob2o10bobobobob59obobobobo
10b2obobo$196b2o4bo6bo3bobobobo61bobobobo3bo6bo4b2o$196b3o3b2o5bo2b3o
2bobobob55obobobo2b3o2bo5b2o3b3o$195bo3bobo2bo5bo3b2obobobo57bobobob2o
3bo5bo2bobo3bo$194bo2bob5o13bobobo2b53o2bobobo13b5obo2bo$196bo4bob2o9b
2obobobobo53bobobobob2o9b2obo4bo$193b4obob2o2b2o7bo3bobobobob51obobobo
bo3bo7b2o2b2obob4o$192b2o8bo10bo2bo2bobobo53bobobo2bo2bo10bo8b2o$212b
2o2bo2bobobobob47obobobobo2bo2b2o$203b2o6bob2o2bobobobobo49bobobobobo
2b2obo6b2o$199b3ob2o5bo3bob3o2bobobo2b45o2bobobo2b3obo3bo5b2ob3o$195bo
b2obo9bo7bob2obobobo45bobobob2obo7bo9bob2obo$194b3o4bo11bo2bob2obobobo
bob43obobobobob2obo2bo11bo4b3o$193bo3bo12b2o9bobobobo45bobobobo9b2o12b
o3bo$194bo14bo13bobobobob39obobobobo13bo14bo$209b2o7bobobo2bobobo41bob
obo2bobobo7b2o$210b3o5bo6bobobo2b37o2bobobo6bo5b3o$210bo2bo3bobo5bobob
obo37bobobobo5bobo3bo2bo$214bo4bo2b2obobobobob35obobobobob2o2bo4bo$
222b2obobobobo37bobobobob2o$209b2obobo10bobobobobob31obobobobobo10bobo
b2o$209b2o3bo9bo2bobobobo33bobobobo2bo9bo3b2o$208bo2bo10b3o2bobobobo2b
29o2bobobobo2b3o10bo2bo$214b5o7b2obobobobo29bobobobob2o7b5o$213bobob2o
10bobobobob27obobobobo10b2obobo$212b2o4bo6bo3bobobobo29bobobobo3bo6bo
4b2o$212b3o3b2o5bo2b3o2bobobob23obobobo2b3o2bo5b2o3b3o$211bo3bobo2bo5b
o3b2obobobo25bobobob2o3bo5bo2bobo3bo$210bo2bob5o13bobobo2b21o2bobobo
13b5obo2bo$212bo4bob2o9b2obobobobo21bobobobob2o9b2obo4bo$209b4obob2o2b
2o6b3ob2obobobob19obobobob2ob3o6b2o2b2obob4o$208b2o8bo5b2ob2o3bob2obob
o21bobob2obo3b2ob2o5bo8b2o$224b2o2bo2bo3bobobobob15obobobobo3bo2bo2b2o
$219b2o2bo2bo7bo2bobobo17bobobo2bo7bo2bo2b2o$215b3ob2o18bobo2b13o2bobo
18b2ob3o$211bob2obo15b2o7bobo13bobo7b2o15bob2obo$210b3o4bo8b2o4bob3ob
2obobob11obobob2ob3obo4b2o8bo4b3o$209bo3bo12b2ob2o4b2o4bobo6bo6bobo4b
2o4b2ob2o12bo3bo$210bo14bo3b2o8bobobobobo5bobobobobo8b2o3bo14bo$229b2o
7bo4bobo2b2ob2o2bobo4bo7b2o$239b2obo15bob2o!

The trick is in the conversion of vertical stripes to horizontal, and then horizontal stripes to vertical, allowing the outer edges of the ship to primarily be supported by period-3 with-the-grain components. But how exactly can a greyship change its stripes?

You may be familiar with the classic 2c/3 signal traveling along a diagonal seam between horizontal and vertical stripes. What you may not realize is that the standard 2c/3 signal is actually made up of two "half signals". On July 24, 1997 Dean Hickerson found a strange p9 signal injector that seemed to inject two signal-like perturbations each period:

Code: Select all

#C A strange p9 signal injector by Dean Hickerson, July 24, 1997
x = 28, y = 29, rule = B3/S23
obo3b2o$2obobo2bo$3bob2obo$3o2bo2bob2o$o2bo3b2obo$b2o8bo$7b4o$b2o3bo$b
o2bo2b6o$3b2obo6bo$4bobo2b5o$2bobobobo7bo$2b2o2bobo2b6o$6bobobo$7b2obo
2b6o$10bobo6bo$10bobo2b5o$11b2obo7bo$14bo2b6o$14bobo8bo$13b2obo2b7o$
16bobo$16bobo2b5o$17b2obo4bo$20bo2bo$20bobob4o$19b2obo4bo$23b3o$25b2o!

These two perturbations are actually oppositely oriented half signals. Unlike a proper signal, a half signal modifies the wire it travels on; it moves the seam between horizontal and vertical stripes to a new location. Below is a comparison of a standard signal and a half signal:

Code: Select all

#C A standard signal (left) and a half signal (right).
#C Notice that the half signal moves the seam between
#C horizontal and vertical stripes upward by 2 cells.
x = 98, y = 40, rule = B3/S23
6b2o2b2o2b2o50b2o2b2o2b2o$6b2o2b2o2b2o50b2o2b2o2b2o2$4b14o46b12o$3bo
14bo44bo12bo$3bobob12o44bob12o$2obobo15bo38b2obo15bo$2obobo2b14o38b2ob
o2b14o$3bobobo55bobo$3bobobo2b14o39bobo2b14o$2obobobobo14bo35b2obobobo
14bo$2obobobobo2b13o35b2obobobo2b13o$3bobobobobo15bo35bobobobo15bo$3bo
bobobobo2b14o35bobobobo2b14o$2obobobobobobo46b2obobobobobo$2obobobobob
obo2b14o30b2obobobobobo2b14o$3bobobobobobobo14bo32bobobobobobo14bo$3bo
bobobobobobo2b13o32bobobobobobo2b13o$4b2obobobobobobo15bo28b2obobobobo
bobo15bo$7bobobobobobo2b14o31bobobobobobo2b14o$7bobobobobobobo45bobobo
bobobobo$6b2obobobobobobo2b14o28b2obobobobobobo2b14o$9bobobobobobobo
14bo30bobobobobobobo14bo$9bobobobobobobo2b13o30bobobobobobobo2b13o$10b
2obobobobobobo15bo28b2obobobobobobo15bo$13bobobobobobo2b14o31bobobobob
obo2b14o$13bobobobobobobo45bobobobobobobo$12b2obobobobobobo2b2o2b2o2b
2o32b2obobobobobobo2b2o2b2o2b2o$15bobobobobobobobo2b2o2b2o35bobobobobo
bobobo2b2o2b2o$15bobobobobobob2o44bobobobobobob2o$16b2obobobobo48b2obo
bobobo$19bobobobo51bobobobo$19bobobobob2o48bobobobob2o$18b2obobobob2o
47b2obobobob2o$21bobobo53bobobo$21bobobo53bobobo$22b2obob2o51b2obob2o$
25bob2o54bob2o$25bo57bo$24b2o56b2o!

Like a standard signal, these half signals can be mirrored across the diagonal stripe seam. Two oppositely oriented half signals are sufficient to put the seam back where it started. This is displayed below, with the half signals separated by a noticeable distance:

Code: Select all

#C Two oppositely oriented half signals do not move
#C the seam between horizontal and vertical stripes.
x = 40, y = 40, rule = B3/S23
6b2o2b2o2b2o$6b2o2b2o2b2o2$4b14o$3bo14bo$3bobo2b11o$2obobobo13bo$2obob
obo2b12o$3bobobobo$3bobobobo2b12o$2obobobobobo12bo$2obobobobobob12o$3b
obobobobo15bo$3bobobobobo2b14o$2obobobobobobo$2obobobobobobo2b14o$3bob
obobobobobo14bo$3bobobobobobobo2b13o$4b2obobobobobobo15bo$7bobobobobob
o2b14o$7bobobobobobobo$6b2obobobobobobo2b14o$9bobobobobobobo14bo$9bobo
bobobobobo2b13o$10b2obobobobobobo15bo$13bobobobobobo2b14o$13bobobobobo
bobo$12b2obobobobobobo2b2o2b2o2b2o$15bobobobobobobobo2b2o2b2o$15bobobo
bobobob2o$16b2obobobobo$19bobobobo$19bobobobob2o$18b2obobobob2o$21bobo
bo$21bobobo$22b2obob2o$25bob2o$25bo$24b2o!

By manually advancing only the second (i.e., upper left most) half signal by 9 generations, the two now-adjacent half signals become one standard signal! But we don't need or want a proper signal here. For making greyships, the movement of the seam is the desirable outcome, it allows the seam to move with the potential ship, so we want subsequent half signals to have the same orientation.

This seam-moving half signal idea was first developed in a discussion between Hartmut Holzwart and Jason Summers from November 2005 to January 2006 after Holzwart incidentally found a 2c/4 seam-moving reaction in an ordinary against-the-grain greyship search. By placing half signals at varying distances, different seam-moving speeds can be achieved. Different placements also need to be used depending on whether the conversion is vertical-to-horizontal (v-to-h) or horizontal-to-vertical (h-to-v). Here are the placements for 2c/6 movement:

Code: Select all

#C 2c/6 stripe converters (travel direction is upward)
#C top left: v-to-h converter
#C bottom    left:  h-to-v converter, homogeneous
#C bottom  middle:  h-to-v converter, heterogeneous
#C bottom   right:  h-to-v converter, heterogeneous
x = 155, y = 89, rule = B3/S23
4bo3bo3bo3bo3bo3bo3bo3bo$3bobobobobobobobobobobobobobobobob2o$3bobobob
obobobobobobobobobobobobobo$b2o2bobobobobobobobobobobobobobobobo$o4bob
obobobobobobobobobobobobobobob2o$b4o2bobobobobobobobobobobobobobobo2bo
$7bobobobobobobobobobobobobobobobo$b6o2bobobobobobobobobobobobobobob2o
$o10bobobobobobobobobobobobobo$b10o2bobobobobobobobobobobobob2o$15bobo
bobobobobobobobobob2o$b14o2bobobobobobobobobobo$o18bobobobobobobobobo$
b18o2bobobobobobobobob2o$23bobobobobobobob2o$b22o2bobobobobobo$o26bobo
bobobo$b26o2bobobobob2o$31bobobob2o$b30o2bobo$o34bo$b34o2$3b2o2b2o2b2o
2b2o2b2o2b2o2b2o2b2o$3b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o12$3b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o26b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o30b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o$3b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o26b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2$b34o22b34o26b34o$o34bo20b
o34bo24bo34bo$b32o2bo21b33obo25b33obo$33bobob2o52bob2o56bob2o$b31obobo
b2o18b31obobob2o22b30o2bobob2o$o32bobo20bo32bobo24bo30bobobo$b30o2bobo
21b30o2bobo25b31obobo$31bobobob2o48bobobob2o52bobobob2o$b28o2bobobob2o
18b29obobobob2o22b29obobobob2o$o28bobobobo20bo30bobobo24bo30bobobo$b
27obobobobo21b27obobobobo25b26o2bobobobo$29bobobobob2o46bobobobob2o48b
obobobobob2o$b26o2bobobobob2o18b26o2bobobobob2o22b27obobobobob2o$o26bo
bobobobo20bo26bobobobobo24bo26bobobobobo$b24o2bobobobobo21b25obobobobo
bo25b25obobobobobo$25bobobobobobob2o44bobobobobob2o48bobobobobob2o$b
23obobobobobobob2o18b23obobobobobobob2o22b22o2bobobobobobob2o$o24bobob
obobobo20bo24bobobobobobo24bo22bobobobobobobo$b22o2bobobobobobo21b22o
2bobobobobobo25b23obobobobobobo$23bobobobobobobob2o40bobobobobobobob2o
44bobobobobobobob2o$b20o2bobobobobobobob2o18b21obobobobobobobob2o22b
21obobobobobobobob2o$o20bobobobobobobobo20bo22bobobobobobobo24bo22bobo
bobobobobo$b19obobobobobobobobo21b19obobobobobobobobo25b18o2bobobobobo
bobobo$21bobobobobobobobob2o38bobobobobobobobob2o40bobobobobobobobobob
2o$b18o2bobobobobobobobob2o18b18o2bobobobobobobobob2o22b19obobobobobob
obobob2o$o18bobobobobobobobobo20bo18bobobobobobobobobo24bo18bobobobobo
bobobobo$b16o2bobobobobobobobobo21b17obobobobobobobobobo25b17obobobobo
bobobobobo$17bobobobobobobobobobob2o36bobobobobobobobobob2o40bobobobob
obobobobob2o$b15obobobobobobobobobobob2o18b15obobobobobobobobobobob2o
22b14o2bobobobobobobobobobob2o$o16bobobobobobobobobobo20bo16bobobobobo
bobobobobo24bo14bobobobobobobobobobobo$b14o2bobobobobobobobobobo21b14o
2bobobobobobobobobobo25b15obobobobobobobobobobo$15bobobobobobobobobobo
bob2o32bobobobobobobobobobobob2o36bobobobobobobobobobobob2o$b12o2bobob
obobobobobobobobob2o18b13obobobobobobobobobobobob2o22b13obobobobobobob
obobobobob2o$o12bobobobobobobobobobobobo20bo14bobobobobobobobobobobo
24bo14bobobobobobobobobobobo$b11obobobobobobobobobobobobo21b11obobobob
obobobobobobobobo25b10o2bobobobobobobobobobobobo$13bobobobobobobobobob
obobob2o30bobobobobobobobobobobobob2o32bobobobobobobobobobobobobob2o$b
10o2bobobobobobobobobobobobob2o18b10o2bobobobobobobobobobobobob2o22b
11obobobobobobobobobobobobob2o$o10bobobobobobobobobobobobobo20bo10bobo
bobobobobobobobobobobo24bo10bobobobobobobobobobobobobo$b8o2bobobobobob
obobobobobobobo21b9obobobobobobobobobobobobobo25b9obobobobobobobobobob
obobobo$9bobobobobobobobobobobobobobob2o28bobobobobobobobobobobobobob
2o32bobobobobobobobobobobobobob2o$b7obobobobobobobobobobobobobobob2o
18b7obobobobobobobobobobobobobobob2o22b6o2bobobobobobobobobobobobobobo
b2o$o8bobobobobobobobobobobobobobo20bo8bobobobobobobobobobobobobobo24b
o6bobobobobobobobobobobobobobobo$b6o2bobobobobobobobobobobobobobo21b6o
2bobobobobobobobobobobobobobo25b7obobobobobobobobobobobobobobo$7bobobo
bobobobobobobobobobobobob2o24bobobobobobobobobobobobobobobob2o28bobobo
bobobobobobobobobobobobob2o$b4o2bobobobobobobobobobobobobobobob2o18b4o
2bobobobobobobobobobobobobobobob2o22b4o2bobobobobobobobobobobobobobobo
b2o$o4bobobobobobobobobobobobobobobobo20bo4bobobobobobobobobobobobobob
obobo24bo4bobobobobobobobobobobobobobobobo$obo2bobobobobobobobobobobob
obobobobo20bobo2bobobobobobobobobobobobobobobobo24bobo2bobobobobobobob
obobobobobobobobo$bobobobobobobobobobobobobobobobobobob2o18bobobobobob
obobobobobobobobobobobobob2o22bobobobobobobobobobobobobobobobobobob2o$
2b2obobobobobobobobobobobobobobobobob2o19b2obobobobobobobobobobobobobo
bobobob2o23b2obobobobobobobobobobobobobobobobob2o$6bo3bo3bo3bo3bo3bo3b
o3bo27bo3bo3bo3bo3bo3bo3bo3bo31bo3bo3bo3bo3bo3bo3bo3bo!

Notice that there is only one 2c/6 v-to-h converter, but there are three h-to-v converters. The bottom left is the "expected" h-to-v converter, where individual half signals all have the same orientation. By contrast, the other two h-to-v converters each have three times as many half signals as the first fitting on the same seam, two with the same orientation and one with the opposite orientation. There's nothing special about any of these h-to-v converters in particular. Amling's ship just happens to use the middle converter.

Of course, it isn't enough to just have these stripe converters. We need to connect them somehow. The difficulty is that these stripe converters are period 6, and 2c/6 searches have little chance of succeeding both because 2c/6 components are rarer than period-3 components and because p6 searches inherently take longer than p3 searches. On May 1, 2021 Holzwart managed to find the symmetric back end shown in the final spaceship, but the back end is almost always the easy part.

Using powerful new search tools, Keith Amling was able to reduce the side and front connection problems from p6 to p3 and then solved them at the lower period. On close inspection, you should be able to see that virtually no part of the connecting components has period 6. It isn't just the period reduction that's impressive here. It would still be quite difficult to complete the p3 parts using previous tools even if the period reduction were given.

Both the speed and the variety of features in Amling's search tools are what sets them apart. Unfortunately, no one else really knows how to use these tools very effectively at the moment. Fortunately (for now) Keith seems sufficiently motivated to solve problems and answer questions about his methods and tools on the forums.

Constructing a 2c/5 against-the-grain greyship is still an open problem.

New Type of c/5 Diagonal Wickstretcher

Keith Amling has found a c/5 diagonal wickstretcher that stretches a period-2 wick consisting of dominoes:

Code: Select all

#C c/5 diagonal domino wickstretcher
#C By Keith Amling, December 8, 2023
#C https://conwaylife.com/forums/viewtopic.php?p=172734#p172734
x = 285, y = 229, rule = B3/S23
81b2o$80bo2bo$79b2o2bo$79bo2b3o$76b2obo2b3o$75b2o5b2o$82b2o$75b2ob5o$
77b5o$73bo$70b2o2bo$70b2o3b2o$68bo3bo4bo$67b3o$65bo2bo4bo3bo$63b2o3bo
5bo$64bo2bobo11bo$63bo2b2ob5o3bob2obo$62bo3b2o3b4ob2o5bo$61bo5bob4o6b
2obo$61b2o4bob3obo5bob2o4bo$60bob2o3bob2o3bobo10b3o$60b3o20b3o3b2o$65b
o19bo3b2o$61bo27bo$63b2o22bobo$91bo$89bo$93bo6b3o$90b2obo5bo$94bobo2bo
b2o$95bobo$97b2o$96bobo6b2o$97b3obo3b2o$97b8obo$99bo4b2o$101bobo3b2o$
100bo2bo2bo2bo$101bo9b2o$102b4o3bo$103b2obo4bo$111bo$105bobo3b2o$111b
2o$113b2o2$113b3o$112b2o$112bo$113bob2o$112b2o6bo$112bob5obo$113b3o5bo
$114bo6bo$119bobo$121bo$121bo$120bob2o$120bo4b2o$121bo4b4o$123b2o2b3o$
126b2o2bo$126bobobo$125b6o$125bo3bo$124b2obo$127bo2bo$128bo2bo$135b2o
9b2o$129b3o2b3o8b2o$129bo3b2o2b2o4b2ob2o$131bobo4b3o2bobo$129b2o2bo4b
3o$140b2obo2b3o$141bob2o2b2o$146b3o$145bo2bob2o$145b3o2b2o$144bo2bo2b
2o$145bo3b2o$147b3o$148bobo$149bo$150bo$150b2o$150bobo$151bo2$150b3o$
150b3o$152b2o8bo$154bo6b2o$154b3o3bo$155b9obo$156bo2bo2bo3bo$103b2o57b
o3bo$29bo27bo4b2o38bo2bo62bo$25b2o3bo26b2o3bo2b2o19b2o6bo10bo$24b2obo
3bo21bo2bo3bo2b3o2bo2bo14b2obob6o3b2o64b2obo$24b4obo8b2o12b2ob3o2bo2bo
5bobo14b2obob2o3bo2bobob2o62bo$30bo3b2ob3o13b2obo8bo3bobobo9b2o9bo2bo
3bo65bo2bo$20b2o11b2o3bobo8bo3b5o8b3o12b2o9bo12bo62bobo$20b2o4b3o3b2o
8bobo3b4obo3bo2bo5bobo4b2o5bo3bo7bo5b3o3b4o61b3o$19bo2bo2bo2bo3bo8bo2b
4o2bo8bo14bo3bobo3bo5bob2o11bob2o61bobo$16b2obo2bo2bo20bo2bo3b3o16bo2b
5o9b2o11b2o2b2obo63bo$22bo9b6ob2obo3b3o5b2o15b2obo8bo6bo3b2o6b2o4bo62b
2o$14b2o3bo2bo9b4ob4ob2o4bo8bo16b4o3bo20bo68b3o$14b2o5bo13b4o2bobo13bo
21b2o24bo$15bob5o22b2o36bo22b2o64bo2b3o$16bo65bo87bo6b2o$105b2obo61b3o
bo$170bob3o$13b3o91b2o62b2o2bo5bo$13bo93b3o67bob3obo$11b2o95bo63bo13bo
$5b2o4bo96bo67b2o5bobob2o$5b3o3bo95b2ob2o61b2o16bo$3bo4bo101b2o67b2o7b
o3bo$3bo3bo102b3o6b2o66bobo2bob2o$7bo105bo4b2obo64b3o3bo3bo$2b2obobo
103bobo2bob2o66bobo2bo4b3o$2o5bo103bo2bobo3b3o67bob2o2bo$2o4b2o108bo4b
obo67bo8b4o$2b4o118bo66bo5b5o3bo$124bobo66b6o2bob2o2b3o$124bobo66bo10b
o5bo2b2o$125bo67bo7b3o3bo2bo7b3o$126bo74b2o4bo3b2ob2o5bo$125bob2o79bo
3b2obo3b3o$125bob2o81bobo5b2o2bo$127bo89bob4o$128b2o88b2obo$129bo89bo$
212bo24bo$130bobo78b2o23bobo$128b2o2bo76b2obobob3o12bo4bo2bo$128b5obo
80bo3bo9bob3o2b2o$127bo2b2o2b2o73bobo2b2o12b2o3bo$126bo3bobobo74bo22bo
bo5b2o$130bobobo92bo6bo4b3o$127b2o4b2o2b3o69bobo3bo3bobo4b2o4bob5o$
132bobo5b2o2bo64bob2o2b2obo2bo10b2obob2o4bob2o$129b3o2b2ob3o2b3o62bobo
6bo2bob2o3b2o6bo8bo$136bo5b2o62b2ob2o3b2o4bo2bob2o15bo5b2o$145b2ob3o
57bo3bo9bobo17bob2o3bo$148b4o56bo34b4o4b2o$144b2o4b3o47bo43bo$144bo3bo
2bo2b2o42b3o4b2obobo33b2o6bo$144b4o2b2o3bo41b2o4b3o4bo33bo$146b2ob2o8b
2o36bo5b2o3bo3bo31bobob3o$150b4obo2bo2bo36b2o5bo6bo30b2obo8b2o$150b2o
3b2obo3b2obobo31bo3bob3o6bo28b2o2bobo2b2ob2o$149b2o3b3o4bob3o34bobo5bo
5bo31bobob4ob3o$154b2o7bo5b4o3bobo21b3o5bo7bo30bo2bob2obob3o$158b3obo
2b2o7b3o20bob2o3bo11bo39bo$166b4o4bo5bo15b3o5bo13bo35bo4bo$169bo3b2obo
bo13b3obo5b2o4bo9bo36b5o$176bobo11b2ob5o10bo11bo35bo4bo$176bobo3bob2o
2b2ob2ob2o6b2obobo12bo40bobo$176bo4bo2b3obo14bobobo14bo37bob2o$180bo4b
2obobo11b3ob3o13bo37bob2ob2obo$177bo24bobob3o15bo38bo5bo$201b2ob3o17bo
35bo5bo3bo$204b3obo17bo34b2o5bo$209bo16bo42b2o$208b2o18bo44bo$208b2o
18bo42bobo3b2o$230bo46bobo$208bo21bo42bobo$207bo2bo21bo43bo$210bo21bo
41bo$205b2o27bo$204b2o28bo40b2o$203b2o3b3o25bo38b6o$202b3o3b3o25bo37bo
3b3o$207b2o29bo36b2ob2o$202b2o2b2ob2o27bo$202b2o2b3o31bo39b2o$204bo35b
o38b2o$242bo36b3o$203bobo3bo32bo38bo$203bob3o2b2o32bo35bob2o$206bo4b2o
31bo36bobo$246bo35bobo$205bo40bo$205b3obo3bo34bo$207b4obo35bo$208bo41b
o$207bo42bo$206b2o44bo$205b2obo2bo40bo$206bo2b2o43bo$206bo4b2o39bo$
209bo41bo3b2o$207b2o2b2o38b2obo$206bo2bobo2b2o$206b2obo$206b2o3bo3bo$
212b3o$204b2o$204b2o9b2o$204b2o11bob2o2bo$201b3o11b2o2b4obo$195b2o4b3o
13b2obobo$195b2ob2o18bobo2bo$195b3obo18bobo$195bo4bo21bo$192b3o2bo2bo
19b3o$192b2o3bo2bo21b3o$191bob4o$191bo7bo23bo$192bo5bo26b2o$226bo2$
224bo$223b2o$223bo$221b2o$215bobo2b2o$214b2obo$214bo3bo$217b2o$212b3o
2b2o$211b2o4b2o$210bo6b2o$210bo2b5o$211b6o$213b2o!

New c/2 Rake Period

Keith Amling has found a p172 line puffer that can easily be cleaned up to form a rake. No c/2 puffer or spaceship of this period was previously known.

Code: Select all

#C p172 c/2 rake
#C Based on a puffer by Keith Amling, December 4, 2023
#C https://conwaylife.com/forums/viewtopic.php?p=172497#p172497
#C https://conwaylife.com/forums/viewtopic.php?p=172604#p172604
x = 87, y = 185, rule = B3/S23
8bo69bo$7b3ob2o61b2ob3o$6b2o3bob2o57b2obo3b2o$5b2o2bo4b5o11b3o9b3o9b3o
11b5o4bo2b2o$6bo5bobobob2obo7bo3bo7bo3bo7bo3bo7bob2obobobo5bo$5b2o6bo
3bo3b2o5b2o3b2o5b2o3b2o5b2o3b2o5b2o3bo3bo6b2o$3b2obob2o9bob3o3b2obobob
2o3b2obobob2o3b2obobob2o3b3obo9b2obob2o$4bobo2b2o6bob2o2b2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2b2obo6b2o2bobo$b2obo2bo2bo4b2o3bo3bobo3b
obo3bobo3bobo3bobo3bobo3bobo3bo3b2o4bo2bo2bob2o$b2obo5b2o2bo3bo49bo3bo
2b2o5bob2o$bobo9bo9b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o9bo9bobo$
2ob2o5b4o4b2o47b2o4b4o5b2ob2o$12bobo2bo3b45o3bo2bobo$20bo3bo5bo21bo4bo
4bo3bo$17b2o49b2o$23bobobobobo19bobo2bobo2bobo$33bo15bo$34bo13bo$35b
13o3$41bo$40b3o$39bo3bo$40b3o$33b2o5b3o5b2o$33b2o13b2o$23b3o7b2o13b2o$
22bo2bo$25bo$25bo9b2ob7ob2o$22bobo13bo5bo$35b2o3bobo3b2o$36b2o3bo3b2o
6$37b2o5b2o$37b2o5b2o$34bo13bo$34bo13bo$34bo13bo12$20b3o37b3o$20bo2bo
35bo2bo$20bo41bo$20bo3bo33bo3bo$20bo3bo33bo3bo$20bo14b2ob2o3b2ob2o14bo
$21bobo11b2ob2o3b2ob2o11bobo2$85b2o$84bobo$86bo6$37bo7bo$37b2o5b2o$36b
4o3b4o$34b2o2b3ob3o2b2o$28b2o4b2o11b2o4b2o$28b2obo3bo3bo3bo3bo3bob2o$
26b3o7b3o5b3o7b3o$30bob2ob4o5b4ob2obo$28bo2b5o11b5o2bo$28bo2bo2b2o11b
2o2bo2bo$27b4o2b2o13b2o2b4o$29bobob2o13b2obobo$31b2o17b2o$31bo19bo7$
26b3o25b3o$17bo6b2o31b2o6bo$16b3o5b2o3bo23bo3b2o5b3o$16bob2o9bo23bo9b
2obo$17b3o5bo31bo5b3o$17b3o6bo2bo23bo2bo6b3o$17b3o6bo2b2o21b2o2bo6b3o$
17b2o7b2ob2o21b2ob2o7b2o$27bobo23bobo$28bo25bo24$21bo39bo$20b3o14b2o5b
2o14b3o$20bob2o13b2o5b2o13b2obo$21b3o10bo13bo10b3o$21b3o10bo13bo10b3o$
21b3o10bo13bo10b3o$21b2o37b2o4$26b3o25b3o$26bo2bo23bo2bo$26bo29bo$26bo
3bo21bo3bo$26bo3bo21bo3bo$26bo29bo$27bobo23bobo3$28bo25bo$27b3o23b3o$
26b2obo23bob2o$26b3o6b2ob2o3b2ob2o6b3o$26b3o6b2ob2o3b2ob2o6b3o$26b3o
25b3o$27b2o25b2o3$30bo21bo$29b3o19b3o$28b2obo19bob2o$28b3o21b3o$28b3o
5bo9bo5b3o$29b2o5bo9bo5b2o$36bo9bo2$30bo7b3ob3o7bo$29b3o19b3o$28b2obo
4bo9bo4bob2o$28b3o5bo9bo5b3o$28b3o3bobo9bobo3b3o$28b3o21b3o$29b2o21b2o
3$32bo17bo$31b3o15b3o$30b2obo15bob2o$30b3o17b3o$30b3o17b3o$31b2o17b2o
4$32b3o13b3o$31bo2bo13bo2bo$34bo13bo$30bo3bo13bo3bo$30bo3bo13bo3bo$34b
o13bo$31bobo15bobo!

New 3c/7 Rake Periods

conwaylife.com user "May13" discovered that a known 3c/7 spaceship could convert a blinker into a glider and used this to construct the first period-42 3c/7 rake:

Code: Select all

#C p42 3c/7 rake using a blinker-to-glider converter
#C By "May13", November 22, 2023
#C https://conwaylife.com/forums/viewtopic.php?p=171661#p171661
#C https://conwaylife.com/forums/viewtopic.php?p=171726#p171726
x = 125, y = 138, rule = B3/S23
60bo7bo$59b3o5b3o$59bobo5bobo$57bobo4bo4bobo$57b2o4bobo4b2o$62bobobo$
61b2o3b2o$60b3o3b3o$56b2o2bo7bo2b2o$56b2obo9bob2o$56bo15bo$58bob2o5b2o
bo$57b2ob2o5b2ob2o$62bo3bo$58bo11bo$57bo4bo3bo4bo$61b2o3b2o$61b2o3b2o$
57bo3bo5bo3bo$57bo3bo5bo3bo$56b2o13b2o$55b2o2bo9bo2b2o$58b3o7b3o$56b2o
2b2o5b2o2b2o$53bo2b2obo2bo3bo2bob2o2bo$53bo4b2obo5bob2o4bo$54b3o2bo9bo
2b3o$55b2ob3o7b3ob2o$55b2o2b2o7b2o2b2o$55b2o15b2o$55b2o2b3o5b3o2b2o$
59bo9bo$55b2o15b2o$59bo2bo3bo2bo$59b2ob2ob2ob2o$51b3o7bo5bo7b3o$51bo2b
o6bo5bo6bo2bo$54b2ob2ob2obobob2ob2ob2o$50bo2bob2obo2bobobobo2bob2obo2b
o$56bobo11bobo$51bobobo17bobobo$52bo2b4o11b4o2bo2$56bo15bo$23b3o9b3o
16bo19bo$23bo2bo7bo2bo14b2o21b2o15b3o9b3o$22b2o13b2o13b2o21b2o15bobo9b
obo$20b2obo3bo5bo3bob2o10bob2o19b2obo13bo2bo9bo2bo$23b3ob2o3b2ob3o13b
2o2bo17bo2b2o13bob4o5b4obo$19bo21bo8b2obo2bo7bo7bo2bob2o10b2o4bobo3bob
o4b2o$20bobob5o3b5obobo9b3ob2o7b3o7b2ob3o11b3ob2obo3bob2ob3o$20bo3bo2b
2o3b2o2bo3bo9b3o3bobo2b2obob2o2bobo3b3o9bo8bo3bo8bo$20bo3b3o7b3o3bo18b
3o2bo2b3o18bobo2b2obo5bob2o2bobo$20bo4bo9bo4bo15bo15bo14bo3b2o4bo3bo4b
2o3bo$24b3o7b3o19bo2b2o3bo3b2o2bo15bobo5bo5bo5bobo$23bo2b2o5b2o2bo17b
2obobo3bo3bobob2o15bo4b3o5b3o4bo$26b2o5b2o20bob2o11b2obo$22b2o4bo3bo4b
2o16bobobob2o3b2obobobo19b2obo5bob2o$21bo3bo3bobo3bo3bo13b3o3bo9bo3b3o
15b2ob2obo3bob2ob2o$18b2ob3obobobobobobob3ob2o10bo21bo15b2ob2ob2ob2ob
2ob2o$17bo5b2o4bobo4b2o5bo9bo21bo12b2o8bobo8b2o$16bo4b2o15b2o4bo9bo4bo
9bo4bo11b2o3bob6ob6obo3b2o$16b3o8bo5bo8b3o8bob4o11b4obo11bobo3b2o9b2o
3bobo$25b2o7b2o16b2o21b2o8bob2o3bo13bo3b2obo$26bo2bobo2bo18bobo17bobo
9bobo6b3o5b3o6bobo$18bo8b2o3b2o8bo10bob2obo11bob2obo9b2o25b2o$15bo3bo
7bo5bo7bo3bo8b6o9b6o22bo3bo$18bo23bo14bo2bo7bo2bo22bo3bobo3bo$13b2o31b
2o10b3o7b3o24bobo3bobo$12bo2b2o27b2o2bo8bo3bo5bo3bo10b3o29b3o$12b2o2bo
27bo2b2o7bo4bo5bo4bo9bo2bo27bo2bo$13b2o2bo25bo2b2o8bo4bo5bo4bo8bo4bo
25bo4bo$14bobo27bobo10b2o11b2o8b2o35b2o$81bobo2bo25bo2bobo$12b3o31b3o
14bobo$12bo6bo11bo16bo15bo16bo2bo29bo2bo$10b2o2bo3bobo9bobo13bo2b2o11b
o3bo14bo2bo29bo2bo$9b2o6b2ob2o7b2ob2o16b2o10bo3bo12bobo35bobo$8bo2bo5b
o15bo15bo2bo8bo5bo10b3o37b3o$7b2o8b3o2bo5bo2b3o18b2o7b2obob2o12bo37bo$
6bo8bo7bo3bo7bo18bo6b2obob2o8bo45bo$6b3o7b2o2b2ob2ob2ob2o2b2o17b3o6bob
obobo7bob2o41b2obo$7b2o7bobo4bo3bo4bobo17b2o6bob2ob2obo6bobo43bobo$13b
3ob3o2b2o3b2o2b3ob3o22bo7bo5b2o47b2o$8bobo2b2ob4ob3o3b3ob4ob2o12bobo6b
2o7b2o5bo47bo$8bobo3b4o4b2o3b2o4b4o13bobo7bo2bobo2bo7b3o41b3o$15bo5b2o
5b2o5bo26b2ob2o10bo43bo$8b2o9bo2bo5bo2bo19b2o11bo$18b3obo5bob3o21bo$
17bo5b2ob2o5bo18bo2b2o7bo11bobo$16b3ob2ob2ob2ob2ob3o17bo3bo6b3o7b2ob2o
$13b2ob2o15b2ob2o16bo2bo5b3o6bobobo$12b2ob2ob2ob4ob4ob2ob2ob2o15bo2bo
18b2o$22b2o3b2o26b2o14bo2bobo$13bo23bo28b2o4bo2bo8bo11bo$10b2ob2o6bo7b
o6b2ob2o21b2obobo5b2o8bobo9bobo$11b2o8b2o5b2o8b2o25bobobo12b2ob2o7b2ob
2o$56b2obo3bob2ob3o11bo15bo$22b3ob3o30b2ob2o6bo11b3o2bo5bo2b3o$9bo31bo
38bo7bo3bo7bo$8b3o29b3o38b2o2b2ob2ob2ob2o2b2o$7b2ob2o27b2ob2o37bobo4bo
3bo4bobo$6b3o33b3o33b3ob3o2b2o3b2o2b3ob3o$6b2o35b2o33b2ob4ob3o3b3ob4ob
2o$6b3o33b3o34b4o4b2o3b2o4b4o$8bo33bo24b2o11bo5b2o5b2o5bo$67b2o15bo2bo
5bo2bo$7b2o33b2o39b3obo5bob3o$4b2obo35bob2o35bo5b2ob2o5bo$4bo2bo35bo2b
o17b2o15b3ob2ob2ob2ob2ob3o$6bo37bo10bo7bo2bo11b2ob2o15b2ob2o$2b2o43b2o
6bo8bo12b2ob2ob2ob4ob4ob2ob2ob2o$bob2o41b2obo5bo31b2o3b2o$bob2o41b2obo
21b2o5bo23bo$2o47b2o22bob2ob2o6bo7bo6b2ob2o$2obo43bob2o25b2o8b2o5b2o8b
2o$2b3o41b3o20bo2bo$2b3o41b3o21bo16b3ob3o$74bo31bo$73b3o29b3o$48b2o22b
2ob2o27b2ob2o$48bob2o19b3o33b3o$50bo20b2o35b2o$47b2o2bo19b3o33b3o$47b
2o24bo33bo$49bo2bo$50b2o20b2o33b2o$69b2obo35bob2o$69bo2bo35bo2bo$53b2o
16bo37bo$51bo3bo11b2o43b2o$56bo9bob2o41b2obo$50bo6bo8bob2o41b2obo$50bo
bobo2bo7b2o47b2o$50bo3bo2bo7b2obo43bob2o$51b2o2b2o10b3o41b3o$52b3o12b
3o41b3o$52b3o!

Keith Amling later found a period-70 puffer which, when combined with known cleaners and converters, allowed the construction of the first p70 3c/7 rake:

Code: Select all

#C p70 3c/7 rake
#C Based on a puffer by Keith Amling, December 4, 2023
#C https://conwaylife.com/forums/viewtopic.php?p=172512#p172512
#C https://conwaylife.com/forums/viewtopic.php?p=172628#p172628
x = 91, y = 288, rule = B3/S23
52bo7bo$50b2ob2o3b2ob2o$50b2ob2o3b2ob2o$53b2o3b2o$49bo5b3o5bo$49bo13bo
$50bo11bo$51b2o7b2o$48bobobobo3bobobobo$48bobob2o5b2obobo$48bobo11bobo
2$53bo5bo$52b2o5b2o$50b2o9b2o$50bo3bo3bo3bo$52bo2bobo2bo$52bobo3bobo$
51bo9bo$49bo3bo5bo3bo$48b4o9b4o$46b2obo2bo7bo2bob2o$46b2o2b3o7b3o2b2o$
49bobo2bo3bo2bobo$47bob3o2bo3bo2b3obo$47bo4bo7bo4bo2$48bo15bo$17b3o9b
3o16b2obo9bob2o$17bo2bo7bo2bo15bo3b2o7b2o3bo$16b2o13b2o$14b2obo3bo5bo
3bob2o12b2o4bo5bo4b2o$17b3ob2o3b2ob3o$13bo21bo14b2ob2o3b2ob2o$14bobob
5o3b5obobo9bo5b2o3bobo3b2o5bo$14bo3bo2b2o3b2o2bo3bo8bob2o5bobo3bobo5b
2obo$14bo3b3o7b3o3bo7b2o2bo3b2obo5bob2o3bo2b2o$14bo4bo9bo4bo9bob2ob6o
3b6ob2obo$18b3o7b3o18bo2bobo3bobo2bo$17bo2b2o5b2o2bo14bobo2bo9bo2bobo$
20b2o5b2o15b3o3bo11bo3b3o$16b2o4bo3bo4b2o11b3obobo11bobob3o$15bo3bo3bo
bo3bo3bo11b3o17b3o$12b2ob3obobobobobobob3ob2o$11bo5b2o4bobo4b2o5bo8bo
19bo$10bo4b2o15b2o4bo5b2o21b2o$10b3o8bo5bo8b3o4bo2bo19bo2bo$19b2o7b2o
13bobo21bobo$20bo2bobo2bo15b3o19b3o$12bo8b2o3b2o8bo18b3o$9bo3bo7bo5bo
7bo3bo8bo5bo3bo5bo$12bo23bob2o4b2o3bo4bobobo4bo3b2o$7b2o28bo4bo2bo2b2o
b2ob5ob2ob2o2bo2bo$6bo2b2o31bo2bo3bobo9bobo3bo2bo$6b2o2bo39bo11bo$7b2o
2bo35bo3b2o7b2o3bo$8bobo35bobo2bobo5bobo2bobo$34bo11bo3bo11bo3bo$6b3o
25bo10bo21bo$6bo27bo9b4o2b2o9b2o2b4o$4b2o2bo35b4o2bo11bo2b4o$3b2o43b2o
13b2o$2bo2bo43bo13bo$b2o$o47bobo11bobo$3o44b2o15b2o$b2o42bobo4bo7bo4bo
bo$46bo3bobo7bobo3bo$2bobo44b3obo5bob3o$2bobo32b2o$48b2o4bo3bo4b2o$2b
2o33b2o13b3o3b3o$53b2o3b2o$35bobo$36bo$36bo$57b3o9b3o$57bobo9bobo$56bo
2bo9bo2bo$56bob4o5b4obo$36bo2b2o13b2o4bobo3bobo4b2o$34b3o2b3o13b3ob2ob
o3bob2ob3o$36bo2b2o12bo8bo3bo8bo$53bobo2b2obo5bob2o2bobo$52bo3b2o4bo3b
o4b2o3bo$41b2o10bobo5bo5bo5bobo$40bobo11bo4b3o5b3o4bo$41bo$58b2obo5bob
2o$56b2ob2obo3bob2ob2o$56b2ob2ob2ob2ob2ob2o$53b2o8bobo8b2o$51b2o3bob6o
b6obo3b2o$52bobo3b2o9b2o3bobo$50bob2o3bo13bo3b2obo$50bobo6b3o5b3o6bobo
$50b2o25b2o$62bo3bo$59bo3bobo3bo$60bobo3bobo$35bo11b3o29b3o$34bobo10bo
2bo27bo2bo$34bobo9bo4bo25bo4bo$35bo9b2o35b2o$46bobo2bo25bo2bobo2$46bo
2bo29bo2bo$46bo2bo29bo2bo$44bobo35bobo$43b3o37b3o$45bo37bo$41bo45bo$
40bob2o41b2obo$40bobo43bobo$39b2o47b2o$36bo3bo47bo$13bo7bo14bo4b3o5bo
7bo27b3o$12b3o5b3o13bo5bo5b3o5b3o27bo$12bobo5bobo25bobo5bobo$10bobo4bo
4bobo21bobo4bo4bobo$10b2o4bobo4b2o21b2o4bobo4b2o$15bobobo31bobobo$14b
2o3b2o29b2o3b2o$13b3o3b3o27b3o3b3o$9b2o2bo7bo2b2o19b2o2bo7bo2b2o$9b2ob
o9bob2o19b2obo9bob2o$9bo15bo19bo15bo$11bob2o5b2obo23bob2o5b2obo$10b2ob
2o5b2ob2o21b2ob2o5b2ob2o$15bo3bo31bo3bo$11bo11bo11bo11bo11bo$10bo4bo3b
o4bo9bobo9bo4bo3bo4bo$14b2o3b2o13bobo13b2o3b2o$14b2o3b2o14bo14b2o3b2o$
10bo3bo5bo3bo21bo3bo5bo3bo$10bo3bo5bo3bo21bo3bo5bo3bo$9b2o13b2o19b2o
13b2o$8b2o2bo9bo2b2o17b2o2bo9bo2b2o$11b3o7b3o23b3o7b3o$9b2o2b2o5b2o2b
2o19b2o2b2o5b2o2b2o$6bo2b2obo2bo3bo2bob2o2bo13bo2b2obo2bo3bo2bob2o2bo$
6bo4b2obo5bob2o4bo13bo4b2obo5bob2o4bo$7b3o2bo9bo2b3o15b3o2bo9bo2b3o$8b
2ob3o7b3ob2o17b2ob3o7b3ob2o$8b2o2b2o7b2o2b2o17b2o2b2o7b2o2b2o$8b2o15b
2o17b2o15b2o$8b2o2b3o5b3o2b2o17b2o2b3o5b3o2b2o$12bo9bo25bo9bo$8b2o15b
2o17b2o15b2o$12bo2bo3bo2bo25bo2bo3bo2bo$12b2ob2ob2ob2o25b2ob2ob2ob2o$
4b3o7bo5bo7b3o9b3o7bo5bo7b3o$4bo2bo6bo5bo6bo2bo9bo2bo6bo5bo6bo2bo$7b2o
b2ob2obobob2ob2ob2o15b2ob2ob2obobob2ob2ob2o$3bo2bob2obo2bobobobo2bob2o
bo2bo7bo2bob2obo2bobobobo2bob2obo2bo$9bobo11bobo19bobo11bobo$4bobobo
17bobobo9bobobo17bobobo$5bo2b4o11b4o2bo11bo2b4o11b4o2bo2$9bo15bo19bo
15bo$7bo19bo7bo7bo19bo$5b2o21b2o4bobo4b2o21b2o$5b2o21b2o4bobo4b2o21b2o
$4bob2o19b2obo4bo4bob2o19b2obo$4b2o2bo17bo2b2o9b2o2bo17bo2b2o$3b2obo2b
o7bo7bo2bob2o7b2obo2bo7bo7bo2bob2o$3b3ob2o7b3o7b2ob3o7b3ob2o7b3o7b2ob
3o$3b3o3bobo2b2obob2o2bobo3b3o7b3o3bobo2b2obob2o2bobo3b3o$12b3o2bo2b3o
25b3o2bo2b3o$9bo15bo19bo15bo$9bo2b2o3bo3b2o2bo19bo2b2o3bo3b2o2bo$8b2ob
obo3bo3bobob2o17b2obobo3bo3bobob2o$8bob2o11b2obo17bob2o11b2obo$8bobobo
b2o3b2obobobo17bobobob2o3b2obobobo$6b3o3bo9bo3b3o13b3o3bo9bo3b3o$6bo
21bo13bo21bo$6bo21bo13bo21bo$7bo4bo9bo4bo15bo4bo9bo4bo$6bob4o11b4obo
13bob4o11b4obo$5b2o21b2o11b2o21b2o$6bobo17bobo13bobo17bobo$6bob2obo11b
ob2obo13bob2obo11bob2obo$7b6o9b6o15b6o9b6o$10bo2bo7bo2bo21bo2bo7bo2bo$
11b3o7b3o23b3o7b3o$10bo3bo5bo3bo21bo3bo5bo3bo$9bo4bo5bo4bo19bo4bo5bo4b
o$9bo4bo5bo4bo19bo4bo5bo4bo$10b2o11b2o10bo10b2o11b2o$35bo$35bo$59bo11b
o$58b3o9b3o$57bo2b2o7b2o2bo$56bo3bobo5bobo3bo$55b2ob2ob2o5b2ob2ob2o$
55b4o3bo5bo3b4o$55bo3b4obobob4o3bo$59bo11bo$54bobo3b2o2bobo2b2o3bobo$
55bo4bobo5bobo4bo2$58b2obo7bob2o$58b5o5b5o$57b2o4bo3bo4b2o$60b4o3b4o$
54bob3obobobobobobob3obo$53b3o2bo5bobo5bo2b3o$52b2o2bo7bobo7bo2b2o$51b
2o3bo4bo7bo4bo3b2o$61bobo3bobo$61bo2bobo2bo$54bo7b2o3b2o7bo$50bob2o23b
2obo$50b4o7bo7bo7b4o$48b2obo27bob2o$47bo2bo29bo2bo$47b2o2bo27bo2b2o$
35bo13b3o27b3o$35bo14b2o27b2o$35bo$48bo33bo$47b3o31b3o$48b2o31b2o$44b
3o37b3o$43bo43bo$43bo2bo37bo2bo$42bo45bo$41b3o43b3o2$44bo41bo$45bo39bo
$43b3o39b3o$44bo41bo$43b2o41b2o$43bo$40b4o$39b2obo$38bo2bo$39b2o$39b2o
$43bo7$36b3o$38bo$33bo3bo$33bo2$37bo$37bo2$35bo4$54b2o$53bobo$55bo11$
71b3o$73bo$72bo10$89b2o$88bobo$90bo!

---endquote---

[dvgrn]

NewLifeCA #45, 14 December 2023: a stable glider-to-LWSS converter, and kickback chain oscillators

...
Finally, a Small G-to-LWSS!
A few days ago Luke Kiernan ran a four-catalyst search on a W (wing) active reaction, and found something that's been overdue to appear for a long time now:  a simple stable conduit with an LWSS output.

Code: Select all

#N W-to-LWSS converter
#O Luke Kiernan, 12 December 2023
x = 14, y = 20, rule = B3/S23
12b2o$4b2o4bobo$4b2o4b2o2$o$3o$3bo$2b2o3$8b2o$8bobo$9bo4$5b2o$6bo$3b3o
$3bo!

This can be combined with a known glider-to-wing converter that Mitchell Riley found back in June of this year, to produce a two-stage stable glider-to-LWSS converter, repeat time 188.  This conduit is a welcome addition to the signal-circuitry toolkit, where it joins Tanner Jacobi's 2015 multi-stage direct Herschel-to-MWSS conduit, along with various older larger slower X-to-spaceship converters.

Code: Select all

#C https://conwaylife.com/wiki/G-to-LWSS_(2023)
x = 65, y = 64, rule = B3/S23
bo$2bo$3o32$47b2o$47b2o2$56b2o$56bobob2o$58bobo$57b2obo$57bo2b2o$58b2o
2bo$59bobo$59bob2o$30b2o26b2obo2bo$30b2o29bob2o$48bo12bo$26bo22bo10b2o
$26b3o18b3o$29bo$28b2o31b2o$48b2o6b2obo2bo$47bobo5bobob3o$34b2o12bo6bo
bo$34bobo16b3ob5o$35bo16bo3bo4bo$52b2o2bobo$43bo13b2o$42bobo2b2o$31b2o
10bo3bobo$32bo16bo$29b3o17b2o$29bo!

Hopefully this isn't the last record-breaking LWSS-producing conduit that we'll see in this decade.  This one is a huge improvement, but an even smaller bounding box and/or shorter repeat time would still be good to have. A few more record-breakers don't seem too unlikely, given the new search spaces that have been opening up recently.

With any luck we'll also start seeing things like elementary conduits with MWSS or HWSS or switch-engine "swimmer" / "bobsled run" outputs.

Kickback-chain oscillators
A bulletin rom the Entertaining New Constructions department:  there has been some collaboration between David Bell, Bullet51, Entity Valkyrie, and JP21 recently on a series of adjustable-period oscillators with a mechanism that involves a single glider initiating a kickback chain reaction in a glider stream.  The mechanism originally showed up in David Bell's newly reduced high-period c/4 spaceships.

Recent reductions in the oscillators have brought the size down to where an example can reasonably be quoted in an email:

Code: Select all

#N P432 kickback-chain oscillator
#O Entity Valkyrie, 14 December 2023
#C https://conwaylife.com/forums/viewtopic.php?p=173320#p173320
x = 109, y = 103, rule = B3/S23
o9bo4bo19bo$3o5b3o4b3o12bo4b3o$3bo3bo10bo7b4obo6bo$2bo2bo2bo8b2o7b3obo
bo4b2o$2bo5bo22bobo$32bo7b2o$3bo3bo23b2o7b2o$4b3o24b2o$16bo14b2o$15b3o
$14bobobo40b2ob2o2b2obo$13b2o3bo23b2o14bobobo3bob2o$4b3o8bobo7b2o15bob
o13bobobobobo3b2o$3bo3bo17bobo14bo14b2ob4obob3o2bo$27bo29bo2bo4bobobob
obo$2bo5bo10bobo5b2o29b2obob2obobo2b2o$2bo2bo2bo11b2o38b2o4bobobo$3bo
3bo12bo42bob2ob2ob2o$bobobobobo23b2obo20b2ob2obo7bobo$obob2ob2obob2ob
2o15b4ob2o18b2ob2obob2ob2obobo$obo7bob2ob2o15bo3b2o26bobobobobo$b2ob2o
b3o4bo21bo5b2o22bo3bo$3bobobo2bob3o18b3o6bobob2o17b2o3b2o$b2o2bobobob
2ob2o4b2o12bo9bobo$obobo3bo7bo3b2o22bobo21bo$bo2bobobob2obob2o3b2o21b
2obobo3b3o12bobo$2b2o3bobo3bobo5bo25b2o2bo3bo10bo3bo$4b2obo3bobobo4bob
o27bo5bo9bo3bo$4bob2o2b2ob2o4b2obo27bo5bo9bo3bo$50bo5bo9bo3bo$51bo3bo
10bo3bo$20b2o30b3o11bo3bo$20b2o45bobo$68bo2$55b2o8b2o3b2o$55bo10bo3bo$
56b3o4b3o5b3o$58bo4bo9bo34$94b2ob2o2b2obo$93bobobo3bob2o$56bob2o2b2ob
2o26bobobobobo3b2o$56b2obo3bobobo11bo12b2o2bobobo2b2o2bo$54b2o3bobobob
obo9b2o13bo2bo4bobobobobo$53bo2b2o2bobobo2b2o24b2ob4obobo2b2o$52bobobo
bobo4bo2bo7bo19bobo2bobobo$53b2o2bobob4ob2o9bo3bo16b4ob2ob2o$55bobobo
2bobo15bo11bo3bobo7bobo$53b2ob2ob4o16b2o11b2ob2obob2ob2obobo$52bobo7bo
bo3bo30bobobobobo$52bobob2ob2obob2ob2o32bo3bo$53bobobobobo19b2o17b2o3b
2o$55bo3bo21bo$54b2o3b2o17b2obo$79bobobo9b3o6b3o$65b2o12bo2b2o4bo5b2o
6b3o$56b3o6b2o10bobo7bobo3bo9bo$56bobo18b2o7b2ob2o$56b3o9b3o15bo2bo$
56b3o9bo2bo15b2o14bo$56b3o9b2ob2o29b3o$56b3o11b2o30b3o$56bobo$56b3o$
90b2o8b2o3b2o$90bo10bo3bo$54b2o3b2o8b2o20b3o4b3o5b3o$55bo3bo10bo22bo4b
o9bo$52b3o5b3o4b3o$52bo9bo4bo!

See the forum thread (link is in the RLE comments) for lots more examples, including variants of the ignition mechanism that can convert these oscillators into guns.

Keep the cheer,


Dave

[dvgrn]

NewLifeCA #46, 30 December 2023: Snark64, c/4d things from p8 through p80, glider synthesis milestones, and an improved upper bound for agars

...
Snark64 and other shiny new conduits
Here's a very nice recent discovery, along the lines of the G-to-X converters mentioned in NewLifeCA #43. Carson Cheng has assembled a drop-in replacement for a Snark, a little bit bigger than the original, with a completely different mechanism involving a transparent beehive. It produces a glider with the same color as a Snark, but a different output timing (19 ticks faster).

Code: Select all

#N Snark64
#O Carson Cheng, 17 December 2023
#C A color-preserving 90-degree reflector with different output parity from the Snark.
#C Repeat time is slightly above the Snark's 43 ticks; it's 64 ticks -- hence the name.
#C https://conwaylife.com/forums/viewtopic.php?p=173506#p173506
#C https://conwaylife.com/wiki/Snark64
x = 28, y = 27, rule = B3/S23
18bo$17bobo$17bob3o$14b2obo4bo$14bobobobobo$16bobob2o4b2o$8b2o5bobo8b
o$8b2o6bo7bobo$24b2o3$13b2o$12bo2bo$13b2o4$b2o$obo$2bo18b2o$8b2o10bob
o$4b2obobo10b2o$4bob2obobo$10b2o3b2o3b4o$15b2o4bo2bo$19bo3b2o$19b2o!

More recently, here's a versatile converter that completes a "partial" by Paul Callahan from more than a quarter century ago. The 1996 "Herschel receiver" always needed a tandem glider as input, or two perpendicular gliders in some cases -- one to activate the transparent block, and one to clean up an annoying extra beehive.

Luke Kiernan turned up a specialized catalyst that can replace one of the fishhook eaters in the Herschel receiver, that improbably manages to shove the active reaction over to delete the annoying beehive, without the catalyst getting in the way of anything. I'm not at all surprised that this catalysis wasn't within reach of 1996 search technology!

Code: Select all

#N boojum reflector variant with 180-degree output at 7hd instead of 9hd spacing
#O Luke Kiernan, 19 December 2023
#C https://conwaylife.com/forums/viewtopic.php?p=173794#p173794
x = 33, y = 52, rule = B3/S23
17b2obo$13b2obo2b2o$13bo3bo$15b2ob2obo$7b2o2b4obobob2o$7bo2bobo$8bobo
$9bobo9b2o$10bo4b2o4bo$15b2o6bo$bo17b5o$2bo16bo$3o19b2o$22bo$20bobo$20b
2o$26bo$24b3o$23bo$23b2o$b2o$b2o6$13b2o$13b2o7$31bo$30bobo$31bo4$21b2o
3b2o$21b2o3b2o3$13bob2o$11b3ob2o$10bo11b2o$11b3ob2o5bo$13bobo7b3o$13b
obo9bo$14bo!

This discovery also implies other related 180-degree reflector variants, one with an output offset of 18hd, and two outputs at 21hd with a 4-mod-8 difference in timing.

These are a little bit large and awkward, but they could possibly become part of some kind of timing adjustment toolkit: it's possible to turn a glider onto an input lane with a Snark without getting in the way of output lanes 18hd or 21hd away. Similarly, connecting this up to the old "glider stopper" catalysis makes a 4hd lane shifter that joins Mitchell Riley's 8hd lane shifter and the 17hd-shifting Bandersnatch in the still very small category of compact stable "0-degree reflectors":

Code: Select all

#N 4hd lane shifter
#C Basically this is the old "glider stopper" without the extra beehive.
#C https://conwaylife.com/wiki/Glider_stopper
#C https://conwaylife.com/wiki/4hd_shifter
#C https://conwaylife.com/wiki/Bandersnatch
#C https://conwaylife.com/forums/viewtopic.php?p=173771#p173771
x = 27, y = 46, rule = B3/S23
17b2obo$13b2obo2b2o$13bo3bo$15b2ob2obo$7b2o2b4obobob2o$7bo2bobo$8bobo
$9bobo9b2o$10bo4b2o4bo$15b2o6bo$bo17b5o$2bo16bo$3o19b2o$22bo$20bobo$20b
2o$26bo$24b3o$23bo$23b2o$b2o$b2o6$13b2o$13b2o14$17b2o$18bo$15b3o$15bo!

The G-to-R version of the converter can also be connected up to the same elementary conduits that a Herschel receiver can, to produce clean R-pentominoes, B-heptominoes, Herschels, and so on -- similar to a syringe or speed tunnel.

New period-8 c/4 technology
Keith Amling's searches have continued to turn up interesting new patterns, such as this impressive c/4 p8 rake, producing a p16 backward glider stream:

Code: Select all

#N period-8 c/4 backrake
#O Keith Amling, 18 December 2023
#C https://conwaylife.com/forums/viewtopic.php?p=173671#p173671
 x = 114, y = 160, rule = B3/S23
20bo$19b2o$19bobo$21bo$22bo$19bob2o$20bo2$21b2o$21b2o$21bo$22b2o2$22b
3o10b2o6b3o$22bo2bo8b2o6bo2b2obo$23bo12bo4bo3b7o$25b2o12bob2o2bo6bo$27b
o9b2o2b3ob2o$20bo7b2o13bob2o2bobo$19b2o19bob2o$19bobo7bo5b3ob2ob2o15b
2o8b2o$29b2o3bo2bo5bo8b3o3b2o9b3o$22b2o7bob2obo3bo3bo7bo7bo4b3o4bo$22b
2o4bo2bo2b4o5b3o8bo10b2o3bobo$29b2o3bob3o3b2o8bobo7bobobo3bo$18bob2o6b
o6bo2bobo3bo4bo2b2o3b8o2bo$17b4o7bobo2bobo9b4obo4bo4b2obobobo$17bo3b2o
8b2o25bo$22bo2bo3bo24bobobo$30b2o$21b2o3bo4bo$21b2o3bob4o2b2obo$22bo5b
obobo4bo$22bo5bo4bo4bo$23b2o6bo4b4o$33bo6bo$31b3o2bo3bo$25bo3b2o2bo2b
o$16b3o4b2o2b2o3b2o4b2o$16bo5bobo3bo4b5o$17bo4b3o3bob4o2bo$19bo8bo5bo
$18b3o5b3o3b2o$23b4o4b3o$17bo2bo2b4o3b3o$15bo9b2ob2obo$14b2ob2obo7b2o
bob2o$14bob5o5bo4bo2bo$12bobob2o7b7o$11b4o3bo5bob4o$11bo2b3o2bo3b2o6b
o$12b2obo10b2o3bo$17b3o3b2o5bo3bo$11b2o4bo3b3o4bobob4o$11b2o3bo3bo7bo
bo2b3o$22b3o$13bo3b2obo4bo10bo$13bo6bo4b3o2b3o2b3o$12bo16bobo2b4o$9b2o
b2o10bo2bobo3b2o$9bo2bo10bo3bobob2o$9bo10b4o7b2o2bobob3o$11bo8bo9b3o2b
5o$10bo15bo14bo$9bo15bo6bo2bo2bo$20b7o6b2o5b2o$4b3o4b2o6bobo12bob2o$4b
o2b4o2bo4b2ob2o10bo$7b3o8bob3o7bo6bobo$bobo11b3o2b2o7b5o6bo$2ob2o2bo7b
o12b2obobo6bo$ob5o20b2o6bo3b2o$2bo11b3o11bo3b3o$bo3b2o9bo9b3obo10bo$b
4o9bobo9b2o3b2o5bo$3b2o9bobo9bo4b2o5b3o$14bobo8b2o4b2o3bobo$15b2o11b2o
2b2ob3o$15bo10bo4b2o3b2ob2o$27b3o6b2o$28b2o2bo3bo3bo$31bo8bo$30bo3b2o
$34b2o$30bo3b2o2bo$29b2ob3o3b2o$38b2o$24b3o6bo2b3o$24bo2b2o4bo2b2o$25b
o2bo8bo$27bo2bo$28b2o8$106b3o$104b2ob2o$87b2o14bo$87bobo3b4o2b3ob3o$87b
o3bo5b4o$90b2o3bobo6b4o$89bo4bobo3bo4bo2bo$89bo2b4obo4b2o$89b2o3bo7b2o
6b3o$83b2ob3o4b3o7b2o5bo$83bo3bo2b2o2bo8b3obo4bo$83bob3ob2o2bo9bo3bo2b
obo$88bob4o8bob2o4b2o$87b3o13b2o2bo2bobo$83b2o3bo4b2obo8bobo$82b2o2bo
4b2obobo8bo2bo$84bobo3bobobo11bo$86bob3ob2o$85b3ob3o14b2o$88b2o4bo11b
3o$94bo13bo$88b2o3bobo12b2o$87b2o5bo2bo10bobo$87bobo3bo7b3o6b2o$86bo2b
o4bo2bo3bo8b2o$95bo6bo10bo$90bo13b2o$87bo2bo14bo2b3obo$87b2o16bo2bo2b
o$88b2ob2o13bob2o$88b2o15b2o$88b2o15b2o$104bo$84b2obo17bobo$83b2o4bo14b
o2bo$85bob2obo15bo$90bo$88bo$88b2o2$88bo$88bo2bo$89b2obo3$84b2ob3o$84b
o3bo$84bob3obo$89b2o$88bo$88bo$85b2o$81bo2b3o$80b3o2bo$79b2o3bo$78b2o
$71b2o6b2o$71bobo3bo2bo$71bo3bo3bo$74b2o$74bo3b2o!

There have been several new constructions based on this -- increasing the period to 72 or 144, converting to block puffers, first known p16 c/4 diagonal spaceship, p80 c/4 puffers and spaceships, and so on. These are a bit hard to summarize, so I'll just suggest looking through the relevant forum thread to see what has showed up there.

Efficient glider syntheses, continued
I mentioned back in February, in NewLifeCA #35, that all 11-bit still lifes had been shown to be synthesizable with no more than six gliders. For almost two years before that, the 180-degree symmetric hook trans-line hook still life, "amphisbaena", had been the final holdout that had needed seven or more gliders.

Since May of this year, amphisbaena was the only 11-cell still life without a known *five-glider* synthesis. On December 10, Alex Greason posted a 5G synthesis. The sequence of cheaper and cheaper syntheses can be seen in the LifeWiki's amphisbaena article.

Along similar lines, back in September 2019, the "17-in-16" project was completed, showing that every 17-bit still life could be constructed using 16 gliders or less. A bit over four years later, on December 26 of this year, Goldtiger997 found the last recipe needed to reduce the upper limit to "17-in-15": All 17-bit still lifes can now be constructed with 15 gliders or less.

Upper bound on agar density reduced to 17/28
The maximum average density of an oscillating agar is conjectured but not proven to be 1/2. Until recently, the lowest upper bound that had been proven was 8/13, by Hartmut Holzwart in 1992.

Forum user '400spartans' has provided a proof that reduces that upper bound very slightly, to 17/28.

-----------------------------------

This is probably getting to the end of NewLifeCA bulletins for 2023 -- though really I just say things like that in hopes of being proven wrong by last-minute discoveries. Other recent news can be found as usual on the LifeWiki main page, or in the news archive.

Happy New Year!


Dave

NewLifeCA #46, 30 December 2023

Addendum:

Average agar density

User NooneAtAll3 has expanded on 400spartans' technique to reduce the lower bound of the maximum average agar density to 320/559 (approximately 0.572).

There are no phoenix oscillators of periods 7, 9, or 11

Recall that a phoenix is a pattern in which all living cells die each generation, but whose population does not reach 0. The most famous phoenix is the following period-2 oscillator:

Code: Select all

....O...
..O.O...
......O.
OO......
......OO
.O......
...O.O..
...O....

Stephen Silver proved in 2000 that period-3 phoenix oscillators were impossible, and in 2019 Alex Greason used a computer search to prove that there are no phoenix oscillators of period 5. Keith Amling has now used his search tools to eliminate period 7 and periods 9 and 11.

2023 oscillator stamp collection

Forum user Entity Valkyrie has completed a comprehensive stamp collection of oscillators above period 12 that were found in 2023. The collection is available here. Notice that there are new oscillators for every period up to 94.

c/5 diagonal wickeater

A c/5 diagonal wickeater to go with Keith Amling's new wickstretcher was surprisingly difficult to find. Here is a solution by Amling with a reduction by Matthias Merzenich:

Code: Select all

#C c/5 diagonal wickeater (shown following a wickstretcher)
#C By Keith Amling, December 13, 2023
#C with reduction by Matthias Merzenich, December 20, 2023
#C https://conwaylife.com/forums/viewtopic.php?p=173181#p173181
#C https://conwaylife.com/forums/viewtopic.php?p=173750#p173750
x = 424, y = 328, rule = B3/S23
81b2o$80bo2bo$79b2o2bo$79bo2b3o$76b2obo2b3o$75b2o5b2o$82b2o$75b2ob5o$
77b5o$73bo$70b2o2bo$70b2o3b2o$68bo3bo4bo$67b3o$65bo2bo4bo3bo$63b2o3bo
5bo$64bo2bobo11bo$63bo2b2ob5o3bob2obo$62bo3b2o3b4ob2o5bo$61bo5bob4o6b
2obo$61b2o4bob3obo5bob2o4bo$60bob2o3bob2o3bobo10b3o$60b3o20b3o3b2o$65b
o19bo3b2o$61bo27bo$63b2o22bobo$91bo$89bo$93bo6b3o$90b2obo5bo$94bobo2bo
b2o$95bobo$97b2o$96bobo6b2o$97b3obo3b2o$97b8obo$99bo4b2o$101bobo3b2o$
100bo2bo2bo2bo$101bo9b2o$102b4o3bo$103b2obo4bo$111bo$105bobo3b2o$111b
2o$113b2o2$113b3o$112b2o$112bo$113bob2o$112b2o6bo$112bob5obo$113b3o5bo
$114bo6bo$119bobo$121bo$121bo$120bob2o$120bo4b2o$121bo4b4o$123b2o2b3o$
126b2o2bo$126bobobo$125b6o$125bo3bo$124b2obo$127bo2bo$128bo2bo$135b2o
9b2o$129b3o2b3o8b2o$129bo3b2o2b2o4b2ob2o$131bobo4b3o2bobo$129b2o2bo4b
3o$140b2obo2b3o$141bob2o2b2o$146b3o$145bo2bob2o$145b3o2b2o$144bo2bo2b
2o$145bo3b2o$147b3o$148bobo$149bo$150bo$150b2o$150bobo$151bo2$150b3o$
150b3o$152b2o8bo$154bo6b2o$154b3o3bo$155b9obo$156bo2bo2bo3bo$103b2o57b
o3bo$29bo27bo4b2o38bo2bo62bo$25b2o3bo26b2o3bo2b2o19b2o6bo10bo$24b2obo
3bo21bo2bo3bo2b3o2bo2bo14b2obob6o3b2o64b2obo$24b4obo8b2o12b2ob3o2bo2bo
5bobo14b2obob2o3bo2bobob2o62bo$30bo3b2ob3o13b2obo8bo3bobobo9b2o9bo2bo
3bo65bo2bo$20b2o11b2o3bobo8bo3b5o8b3o12b2o9bo12bo62bobo$20b2o4b3o3b2o
8bobo3b4obo3bo2bo5bobo4b2o5bo3bo7bo5b3o3b4o61b3o$19bo2bo2bo2bo3bo8bo2b
4o2bo8bo14bo3bobo3bo5bob2o11bob2o61bobo$16b2obo2bo2bo20bo2bo3b3o16bo2b
5o9b2o11b2o2b2obo63bo$22bo9b6ob2obo3b3o5b2o15b2obo8bo6bo3b2o6b2o4bo62b
2o$14b2o3bo2bo9b4ob4ob2o4bo8bo16b4o3bo20bo68b3o$14b2o5bo13b4o2bobo13bo
21b2o24bo$15bob5o22b2o36bo22b2o64bo2b3o$16bo65bo87bo6b2o$105b2obo61b3o
bo$170bob3o$13b3o91b2o62b2o2bo5bo$13bo93b3o67bob3obo$11b2o95bo63bo13bo
$5b2o4bo96bo67b2o5bobob2o$5b3o3bo95b2ob2o61b2o16bo$3bo4bo101b2o67b2o7b
o3bo$3bo3bo102b3o6b2o66bobo2bob2o$7bo105bo4b2obo64b3o3bo3bo$2b2obobo
103bobo2bob2o66bobo2bo4b3o$2o5bo103bo2bobo3b3o67bob2o2bo$2o4b2o108bo4b
obo67bo8b4o$2b4o118bo66bo5b5o3bo$124bobo66b6o2bob2o2b3o$124bobo66bo10b
o5bo2b2o$125bo67bo7b3o3bo2bo7b3o$126bo74b2o4bo3b2ob2o5bo$125bob2o79bo
3b2obo3b3o$125bob2o81bobo5b2o2bo$127bo89bob4o$128b2o88b2obo$129bo89bo$
212bo24bo$130bobo78b2o23bobo$128b2o2bo76b2obobob3o12bo4bo2bo$128b5obo
80bo3bo9bob3o2b2o$127bo2b2o2b2o73bobo2b2o12b2o3bo$126bo3bobobo74bo22bo
bo5b2o$130bobobo92bo6bo4b3o$127b2o4b2o2b3o69bobo3bo3bobo4b2o4bob5o$
132bobo5b2o2bo64bob2o2b2obo2bo10b2obob2o4bob2o$129b3o2b2ob3o2b3o62bobo
6bo2bob2o3b2o6bo8bo$136bo5b2o62b2ob2o3b2o4bo2bob2o15bo5b2o$145b2ob3o
57bo3bo9bobo17bob2o3bo$148b4o56bo34b4o4b2o$144b2o4b3o47bo43bo$144bo3bo
2bo2b2o42b3o4b2obobo33b2o6bo$144b4o2b2o3bo41b2o4b3o4bo33bo$146b2ob2o8b
2o36bo5b2o3bo3bo31bobob3o$150b4obo2bo2bo36b2o5bo6bo30b2obo8b2o$150b2o
3b2obo3b2obobo31bo3bob3o6bo28b2o2bobo2b2ob2o$149b2o3b3o4bob3o34bobo5bo
5bo31bobob4ob3o$154b2o7bo5b4o3bobo21b3o5bo7bo30bo2bob2obob3o$158b3obo
2b2o7b3o20bob2o3bo11bo39bo$166b4o4bo5bo15b3o5bo13bo35bo4bo$169bo3b2obo
bo13b3obo5b2o4bo9bo36b5o$176bobo11b2ob5o10bo11bo35bo4bo$176bobo3bob2o
2b2ob2ob2o6b2obobo12bo40bobo$176bo4bo2b3obo14bobobo14bo37bob2o$180bo4b
2obobo11b3ob3o13bo37bob2ob2obo$177bo24bobob3o15bo38bo5bo$201b2ob3o17bo
35bo5bo3bo$204b3obo17bo34b2o5bo$209bo16bo42b2o$208b2o18bo44bo$208b2o
18bo42bobo3b2o$230bo46bobo$208bo21bo42bobo$207bo2bo21bo43bo$210bo21bo
41bo$205b2o27bo$204b2o28bo40b2o$203b2o3b3o25bo38b6o$202b3o3b3o25bo37bo
3b3o$207b2o29bo36b2ob2o$202b2o2b2ob2o27bo$202b2o2b3o31bo39b2o$204bo35b
o38b2o$242bo36b3o$203bobo3bo32bo38bo$203bob3o2b2o32bo35bob2o$206bo4b2o
31bo36bobo$246bo35bobo$205bo40bo$205b3obo3bo34bo$207b4obo35bo140bo$
208bo41bo137b4o$207bo42bo135b2obob2o$206b2o44bo133b2o2b2o$205b2obo2bo
40bo132bo5bo$206bo2b2o43bo128b2ob2o4b2o$206bo4b2o41bo128b2o3bo4bo$209b
o46bo128bo3b2o$207b2o2b2o43bo132b2o$206bo2bobo2b2o42bo127b2o$206b2obo
48bo129b5o$206b2o3bo3bo44bo127b2o4b2ob3o$212b3o45bo130b2ob3obob2o$204b
2o56bo129bo5b5o$204b2o9b2o45bo129b3o3bo5bo$204b2o11bob2o2bo40bo128bobo
bo5bobo$201b3o11b2o2b4obo39bo134b2o$195b2o4b3o13b2obobo43bo132b2o4b3o$
195b2ob2o18bobo2bo42bo131b2o$195b3obo18bobo47bo129bobo6bobo3b2o$195bo
4bo21bo45bo130bo9bob2o2bo$192b3o2bo2bo19b3o47bo136b2o$192b2o3bo2bo21b
3o45bo135b2o7bo$191bob4o75bo133bo5bo2bo$191bo7bo23bo48bo139bo3b2ob2o$
192bo5bo26b2o47bo138bob3o3bo$226bo47bo142bobo2bo$276bo146bo$224bo51bo
105bo10bo27bobo$223b2o53bo100b2obo10bo28bo$223bo54bo100bo9bo2bo2bobo$
221b2o57bo98bobo6bob3obobobo20b3o$215bobo2b2o58bo99b2o2b2obo3b2o26b3o$
214b2obo64bo97b2obo3bob2obo19b2o8bo$214bo3bo63bo93b2o3b2o10b2o9bo7bo7b
o$217b2o65bo88b2o7bo4bo4bobo6b2ob2obo6bo5bo$212b3o2b2o65bo87b2o2bob2o
3bo2b2ob5o5b2o3bobobo2b3obo$211b2o4b2o67bo80b2o4bo5bo2b2o4bo4b2o3bo3b
4obo3b2o5b3o$210bo6b2o67bo78b3obobobo3b3o2b2o9bob2ob4o3bob2o7b2ob3o$
210bo2b5o70bo75bo16bob2o18bo3b3obo6bob3o$211b6o71bo74bo3b3o3bo20b3o6bo
2bo2bobo$213b2o75bo72bo2bo5bo32bo$290bo72bobo$292bo72bo$292bo72bo$294b
o67b2ob2o$294bo65b2obob2o$296bo66b2ob3o$296bo60b2o3bo3bobo$298bo57b2o
3bo4bobo2bobo$298bo56bo3bobo9bo2b2o$300bo55b3o12bobo2bo$300bo51bo3bobo
3bo13b2o$302bo49bo2bo2bobo$302bo48bo2bo2b3o15bo$304bo45bo5b3o16b3o$
304bo45bobo3b2o19bo$306bo43b3o$306bo40b2o23b3o2b2o$308bo27bo9b2obo21bo
$308bo25b2obo7b2ob2o20bo5bo$310bo23bo10bo24bo5bo$310bo23bo4bo2bo2bo25b
2obo$312bo10b2o11bo5bobo25b3o2bob2o$312bo10b2o7b2ob2ob2o2bobo26bo5bo$
314bo7bo2bo6bob2o2bo39bo$314bo5b2ob2o8b2o4bo4bobo24b2o$316bo3b5o2bobo
4bo5bob2o2bo23b3o$316bo8b2ob3ob2obo3b2ob2o8b2o16bo3b2o$318bo7b2obo2b3o
b2o2bo2bo3b2ob2o2bo15b3o$318bo7bo2bo7b3o2bob2o3b2obo17b2o7b2o$320bo7b
2o8b2ob3o8bo18bo5bo3bo$320bo7b3o6bo5bo27b2obob2o2bo$322bo7bobo17bobo
18bo4bo$322bobo7bo17bobo19bo4bo2bo$324bo24bo27bobo$323bobo23bo3b2o21bo
b2o$322b2o29bo2bo19bobo$321bobo26b2obo3b2o18b2o$318b2obo31bo3b2o19bo$
318bo2bo30b2o3bo20bo$320bo31b2obobob2o16bo$319b2o2bo30b5o2bo16b2o$319b
2obobo29bo2bo2b2o$319b4o37b2o$319b2o2bobo29b3o2b2o$319b3o2b2o30bobob2o
$320bobo33bo6b2o4b2o$322bo35bo4b2o2b2o2bo$320bobo37bob2obo2b5o$320b2o
43bo4b3o$319b2o3b2o39bo3b3o$324b2o42b2o$318b3o3bo42b2o7bo$319b4o44b3o
5b2o$320b3o51bo$321bo49bobob2obo$319b3o47bo3bo2bo$318b2ob2o46b2o7bo2bo
$321b2o50b2o4bo2bo$318b3o2b2o53b2ob2o$320b2o3bo55bobo$320b2obo$320bo2b
2o58bo$320bobo60bo$322b2o58bo2bo$319bo2bo60bobo$319bo2bo59b2ob2o$318bo
2bo59bob3o$317b5o58b2o3b2o$318bo60bo3bobobo$317bo5bo55bobo6bo$317bo4bo
57bo6b2o$318b2obo65b3o$388bo2bo$316bo70b2obobo$315b2obo69bo4bo$316b2o
70bob2ob2o$314bo73b2o3b2o$305b3o4b2o72b2obo3bo2bo$304bo6bo5bo68b3o2bo
2bo$303bo2b2o2bo3b2obo72bo5bo$301b2obob2o4bo5bo71bo$300bo2bo2b2o10bo
72bobo$300bo3bobo11bo$300bob2obo14bo71bob4o$301bobo16b2o70bo3b2o3b2ob
2o$301b4o15bobo75bob2ob2obo$300b5o18bo74bobo4b3o$299b2o3bo17bob3o73bo
2bob2o$298bo2bo23b2o76bobo$297bo2bo104bo$296bo108bo$290b3o2b2obo107bo$
289bo3b3obo$289bo2bob2o$288bobob4o$287bobobo2b3o$286bo5bo$286bob4o$
286bob3o!

Also, here's an item from the efficient-glider-syntheses department that I missed in my previous summary: the following 9-glider synthesis completed the "15-in-10" project, meaning that all 15-bit still lifes can now be constructed with ten gliders or less.

Code: Select all

#N xs15_31248a51246 synth
#O Carson Cheng, 22 December 2023
#C This was the final "expensive" 15-bit still life that had cost
#C more than ten gliders to synthesize.
#C https://catagolue.hatsya.com/object/xs15_31248a51246/b3s23
x = 72, y = 29, rule = B3/S23
48bo$49b2o$48b2o9$2bo$obo$b2o7bo42bo$8b2o44b2o$9b2o42b2o10bo4b2o$64bob
o2bobo$14bo50bo2bo$13bo52b2o$13b3o39b3o$9b2o46bo$bo6bobo45bo$b2o7bo$ob
o3$50b3o$52bo$51bo!