NewLifeCA discussion thread

[dvgrn]

This is a secondary thread associated with the locked NewLifeCA Back Issues archive thread. See the first post of that thread for an explanation of what the NewLifeCA group is.

NewLifeCA discussion and comments are set up here as a separate thread, just to keep the Back Issues thread from getting cluttered with things that aren't actually back issues.

[pcallahan]

I completely forgot about my self-destructing switch engine pair referenced in a back issue. Thanks for the reminder. I'm surprised I had the tools compiled and running to find it in December 2019. I wonder if a similar approach makes a much longer methuselah.

Another methuselah-ish question came to mind recently. Are there small patterns that run chaotically for a long time, appearing to be methuselahs but then generate an infinite growth switch engine instead of stabilizing? I'm sure there are some depending on the definition of "small", "chaotically", and "long", but usually if a switch engine appears, it shows up pretty soon. What's the longest it takes for one to show up? (excluding patterns designed to do this)

[dvgrn]

Another methuselah-ish question came to mind recently. Are there small patterns that run chaotically for a long time, appearing to be methuselahs but then generate an infinite growth switch engine instead of stabilizing?

Unfortunately our main source of smallish methuselah patterns these days is apgsearch -- but if I remember correctly, apgsearch doesn't count a pattern as a methuselah if it ends with infinite population growth.

We could certainly make a hacked version of apgsearch that went back and checked every GPSE and BLSE output, and recorded the time that the population mod 1152 started increasing linearly.

Even if standard apgsearch started collecting these things, presumably the record-setting methuselah-ish pattern of that type would tend to trail the current 16x16 methuselah record-setter by several thousand ticks, just due to the small proportion of 16x16 patterns produce infinite growth. So... I'm thinking it might not be too surprising if someone could come up with a MEIG (Methuselah Ending with Infinite Growth) with a non-boring lifespan in the 30,000s, or maybe even in the 40,000s -- but a 50,000+ lifespan would be surprising and impressive.

[igblan]

Back into the fray. Dave Greene recommended I post this stuff here.

I was inspired by the D8_4 collidoscopes in the Methuselah-ish Symmetric Soups thread, mentioned by Dave in a recent NewLifeCA post.

Yesterday and today I've been investigating (watching) what happens if you run the 64m-tick pattern for a bit, then replace the centre with a randomly-generated D8_4-symmetric or asymmetric pattern.

Glossary:
Bihivite: The crystal sometimes formed by an even-period glider stream, with two beehives per layer.
Drill-bit: The site where the leading glider in a stream interacts with debris.
Drilling: The process whereby the drill-bit pushes downstream through debris or by bihivite erosion.
Silting: The process whereby the drill-bit is pushed upstream by bihivite accretion or a detonation.
River: A pair of parallel streams.

The symmetric patterns unsurprisingly resemble the patterns in the D8_4 soup collection. Drilling appears to outpace silting in the long run. Even if a stream silts up a long way from the centre, the drill-bit always seems to find its way back.

The asymmetric patterns are much more interesting. The two streams in a river occasionally silt each other up. This is enough to reverse the long-term trend, and the river accumulates more and more silt, while the drill-bit slowly moves upstream. The initial asymmetry in the centre slowly creeps up the rivers with the silting.

But if one stream gets blocked by some kind of eater, the other resumes its net drilling. Sometimes it drills right though the centre and through the opposite arm. If it meets another stream head-on, their gliders simply cancel. But if that stream's partner is still active, silt is occasionally thrown in the path of the head-on gliders, and they resume drilling, only to meet head-on again in a different place.

If two offset streams meet (ie each is the 180-degree rotation of the other), they battle it out head to head (this is where I am with my current run, 124m ticks in, with all but two streams quiescent). If the drill-bits pass each other, one will soon silt up the other. The current site of the battle is almost certainly following a symmetric random walk.

Here is some code.

Code: Select all

-- Experiments with randomly generated symmetric and asymmetric
-- D8_4-like collidoscopes.

g = golly()

g.new("D48")

g.setcursor("Move")

g.setrule("b3/s23")
g.setalgo("HashLife")
g.setbase(2)
g.setstep(6)
g.setmag(0)

g.autoupdate(true)

local d84 = g.parse(
[[bo4bobo2bo8bo2bobo4bo$2o2bo2bobob2obo2bob2obobo2bo2b2o$3b2ob4obo2bo2bo
2bob4ob2o$2bo2bo5b2ob4ob2o5bo2bo$b2obobo3bob2ob2ob2obo3bobob2o$3bo9bob
2obo9bo$obobobo3bob3o2b3obo3bobobobo$b2o6bo4bo2bo4bo6b2o$obo5b5obo2bob
5o5bobo$b2o4b7ob2ob7o4b2o$4bobob2ob2o6b2ob2obobo$4o4b5ob4ob5o4b4o$bob
2obob4o2b4o2b4obob2obo$4b3o2bo3b2o2b2o3bo2b3o$b3o2b3o2b10o2b3o2b3o$3b
3o3bob2ob4ob2obo3b3o$3b3o3bob2ob4ob2obo3b3o$b3o2b3o2b10o2b3o2b3o$4b3o
2bo3b2o2b2o3bo2b3o$bob2obob4o2b4o2b4obob2obo$4o4b5ob4ob5o4b4o$4bobob2o
b2o6b2ob2obobo$b2o4b7ob2ob7o4b2o$obo5b5obo2bob5o5bobo$b2o6bo4bo2bo4bo
6b2o$obobobo3bob3o2b3obo3bobobobo$3bo9bob2obo9bo$b2obobo3bob2ob2ob2obo
3bobob2o$2bo2bo5b2ob4ob2o5bo2bo$3b2ob4obo2bo2bo2bob4ob2o$2o2bo2bobob2o
bo2bob2obobo2bo2b2o$bo4bobo2bo8bo2bobo4bo!]], -16, -16)

g.putcells(d84)

local function randfill(percentage)
  local rect = g.getselrect()
  local cells = {}
  for x = rect[1], rect[1] + rect[3] - 1 do
    for y = rect[2], rect[2] + rect[4] - 1 do
      if 100 * math.random() < percentage then
        table.insert(cells, x)
        table.insert(cells, y)
      end
    end
  end
  g.putcells(cells)
end

local symmetric = false

if symmetric then

  ------------------------ Symmetric experiments -----------------------

  local initrun = 2048
  local soupradius = 64

  -- math.randomseed(12345678) -- 10m bihivite inhibitor
  -- math.randomseed(723894987) -- ?m Jedi
  -- math.randomseed(4715627838947) -- 3m Jedi
  -- math.randomseed(167283476) -- 11m bihivite inhibitor

  math.randomseed(46456387162) -- 13m inline eater

  g.run(initrun)

  g.select{-soupradius, -soupradius, 2 * soupradius, 2 * soupradius}
  g.clear(0)

  rect = {0, 0, soupradius, soupradius}
  g.select(rect)
  randfill(25)
  g.select{}
  cells = g.getcells(rect)
  g.putcells(cells, 0, 0, 0, 1, 1, 0, "xor") -- Reflect in x=y
  cells = g.getcells(rect)
  g.putcells(cells, -1, 0, 0, -1, 1, 0)   -- Rotate
  g.putcells(cells, -1, -1, -1, 0, 0, -1) -- Rotate
  g.putcells(cells, 0, -1, 0, 1, -1, 0)   -- Rotate

else

  ----------------------- Asymmetric experiments -----------------------

  local initrun = 2048
  local soupradius = 16

--  math.randomseed(46456387162) -- 83m 6 blocked streams, 2 streams colliding
--  math.randomseed(266785872) -- 81m 4 blocked streams, 1 dead branch, 1 neutered branch
  math.randomseed(177416229) -- 124m and counting, 1 dead branch, 4 blocked streams, 2 stream battling

  g.run(initrun)

  g.select{-soupradius, -soupradius, 2 * soupradius, 2 * soupradius}
  g.clear(0)
  randfill(25)
  g.select{}

end

Cheers, Paul

Edit: PS. You can run these patterns zoomed out and sped up quite a bit (eg zoom 2^6, step 2^10), and still see what's going on. Active drill sites tend to throw off gliders, so you can get an idea of where the drill-bits are, and whch branches might've become quiescent.

Edit: PPS. 0849 Zulu: The last experiment above stabilized after 202m ticks, with the battling streams eventually blocked by eaters. Coffee time, then I might try windmill symmetry for the random centre.

[igblan]

Very interesting dynamics in the asymmetric branch with

Code: Select all

math.randomseed(41159898)

129m ticks to stability. But fairly early on an upstream glider on the NE branch collides with the "flare" sent out by the ark, neither destroying nor neutering it, but causing a "lump" to appear which silts up the river, and later the SW branch produces a stream which drills all the way through to that lump. On top of that, another lump is produced by a circumferenatial xWSS from one of the other branches in roughly the same place.

I might write a script to survey the possible interactions between this ark and upstream gliders which just shave past the downstream gliders. I'd seen killing and neutering interactions before, but never one that left the ark alive and potent.

Cheers, Paul

[Sokwe]

NewLifeCA #23: 7/9/2022 10:28pm

non-trivial oscillators have been found for the two periods (p34 and p38) where only trivial ones were known at the beginning of this year.

There are no known p19 oscillators, so there were no known trivial p38 oscillators at the beginning of the year.

[dvgrn]

There are no known p19 oscillators, so there were no known trivial p38 oscillators at the beginning of the year.

True enough! I can't fix the emails that already went out, but it's nice that I can edit in a note to the back-issue thread.

I made another mistake in the email, which I'll probably mention in the next email: the intention was to quote the p74 pi-heptomino oscillator in the form where it briefly contains an extra fishhook eater, so I put that in the comments -- but instead I sent out a pattern with a couple of different stabilization variants. For that one I just went ahead and fixed the Back Issue, so that the comments make sense there.

EDIT: That's funny, I knew the c/6 spaceship was diagonal. Must have somehow typed it wrong anyway.

[May13]

NewLifeCA #23: 7/9/2022 10:28pm

relatively small new c/6 orthogonal spaceship by May13, 9 July 2022, with one part in common with a known pushalong for another spaceship, 77P6H1V1

Another mistake: new spaceship is diagonal.

[HartmutHolzwart]

No update to this during my August holidays?

[dvgrn]

No update to this during my August holidays?

Not yet! I started to write something yesterday, but August discoveries are tricky to summarize in any kind of short form... and I've been doing a lot of holiday-ing as well.

[HartmutHolzwart]

That's nice! It's just hard to get an overview if you've not followed the developments for a month...

I always love your summaries!

[dvgrn]

That's nice! It's just hard to get an overview if you've not followed the developments for a month...

Relying on my summaries has a serious drawback, though. There's a lot going on, and I'm not a properly unbiased editorial team.

So no doubt I'll be more likely to mention developments that I'm personally the most interested in, and fail to include things that I'm not so excited about (or that I just don't understand very well).

-- But I guess this is just the way this NewLifeCA project is going to have to work for the time being. If I forget anything really big and obvious, an email or forum PM to me might be a good idea -- a ping or two every few months won't do me any harm, and might make for a better news archive in the long run.

[Sokwe]

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

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

...

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!

...

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.

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".

[Sokwe]

EDIT by dvgrn: Sent as NewLifeCA #39, 25 June 2023 9:16am.

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!

Here are some of the smaller items.

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!

[Sokwe]

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

Addendum: EDIT by dvgrn: sent to NewLifeCA email list, 6/26/2023 6:44am.

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?

[Sokwe]

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

Here is a proposed issue #42. There are some large RLEs and I'm not sure how it would need to be reformatted for email.

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.

[Sokwe]

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

Your latest NewLifeCA issue has reminded me of a write-up I had intended to create for the c/3 against-the-grain greyship. Here is that write-up along with some additional discoveries as a proposed issue #44:


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!

[NooneAtAll3]

have "LiveCA private mailing list"'s news articles been uploaded anywhere?

[dvgrn]

have "LiveCA private mailing list"'s news articles been uploaded anywhere?

No. Unfortunately there are old privacy limitations associated with those email archives, so they can't be made publicly available.

A number of people currently active on the forums were members of the old LifeCA mailing list, though, so most questions relating to those archives either have been answered, or can be answered.

[NooneAtAll3]

Unfortunately there are old privacy limitations associated with those email archives

even without discussion mail, only news summaries (aka topic starters)?

I don't know how email discussion works

[Sokwe]

Unfortunately there are old privacy limitations associated with those email archives

even without discussion mail, only news summaries (aka topic starters)?

The original LifeCA mailing list didn't have news summaries. These news summaries are simply a service Dave Greene is providing to the original LifeCA members who aren't on the forums.

Edit: I guess there were news summaries in the last decade or so, but I must have forgotten about them, as I kept up with all the current news without the need for summaries.

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).
viewtopic.php?p=174190#p174190

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 periods 7, 9, and 11.
viewtopic.php?p=172934#p172934
viewtopic.php?p=172938#p172938

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!

[dvgrn]

The original LifeCA mailing list didn't have news summaries. These news summaries are simply a service Dave Greene is providing to the original LifeCA members who aren't on the forums.

Edit: I guess there were news summaries in the last decade or so, but I must have forgotten about them, as I kept up with all the current news without the need for summaries.

Let's see... Between 2010 and 2020 there were occasional short LifeCA discussions about various topics. But for the most part, active discussions shifted very quickly from LifeCA over to the conwaylife.com forums, as soon as the forums showed up in 2009. I think that posts in the 2010s were usually either intermittent news summaries, often from me but occasionally from someone else -- or they were nominations of new members, to give more people access to the older email archives.

There are no privacy restrictions on anyone publicly posting their own emails to LifeCA (except for some weird grey areas when an email quotes someone else's post). So it would probably work for me to extract all of the news summaries that I wrote, from the 2010-2020 period at least, and put them in a forum thread somewhere.

I haven't gone back and looked at that specific material for quite a while, so I don't know if it would really be interesting or useful enough to be worth making public at this point. A lot of that material also ended up on the LifeNews blog on pentadecathlon.com -- which is also probably in some danger of becoming less accessible over time, so it could really stand to be LifeViewer-ified and copied to some other location, maybe a new subfolder of conwaylife.com/ref/.

NewLifeCA #46, 30 December 2023

Addendum...

Thanks for the summary! I'll get this sent out now.

[NooneAtAll3]

A lot of that material also ended up on the LifeNews blog on pentadecathlon.com -- which is also probably in some danger of becoming less accessible over time.

pentadecathlon.com gives me 403 Forbidden

[confocaloid]

A lot of that material also ended up on the LifeNews blog on pentadecathlon.com -- which is also probably in some danger of becoming less accessible over time.

pentadecathlon.com gives me 403 Forbidden

I believe the best remaining way to access pentadecathlon.com is via Wayback Machine:
https://web.archive.org/web/20160912105 ... /lifeNews/

See forum thread "Pentadecathlon.com down" for additional context.

[Sokwe]

It's probably about time for another NewLifeCA issue or two. I intend to write up an issue on the new c/4 diagonal technology soon (especially given today's new discoveries). Before that, there should be an issue covering the various other Life results, including the following (from the news archive):

• Adam P. Goucher's Proof that every finite phoenix has period 2
• Keith Amling's reduction of the average agar density upper bound
• 400spartans' smaller unique father solution
• JP21's and others' new 2c/3 signal injectors
• Goldtiger997's synthesis of 77P6H1V1
• p53 gun by iNoMed, based on a partial result by goldenratio
• p15 and p16 guns by Period1GliderGun using oscillators by Carson Cheng and Nico Brown respectively
• p16 independent reflector by James Pascua
• p26 independent reflector by Period1GliderGun
• New p19 oscillator/wick by Period1GliderGun based on a partial result by iNoMed
• Keith Amling's p9 c/3 rake
• Keith Amling's p6 c/2 coiled snake stretchers and coiled snake and table greystretchers

It doesn't have to be Dave or me. Anybody who wants can write up an issue for the old-timers on the mailing list, using past issues as a guide. I suppose I'll eventually write it up myself if nobody else does.

Edit: added some news items