ConwayLife.com • Building a reverse caber-tosser - Page 7

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Re: Building a reverse caber-tosser

Posted: June 28th, 2018, 1:58 pm

by calcyman

It looks like 59 should be 58, anyway, so that's fine...

Re: Building a reverse caber-tosser

Posted: June 30th, 2018, 8:11 am

by chris_c

I have a redesign in mind that should remove two further switch engines and take us down to 50 gliders in total.

First I found a puffer with a 7G synthesis that can reflect a single glider. The source of the puffer was this post by Saka. That should allow us to remove one of the NW travelling switch engines:

Code: Select all

x = 114, y = 167, rule = B3/S23
bo$2bo$3o22$22bo$20bobo$21b2o$25bo$24bo$24b3o6$28bo$27b2o$27bobo4$12bo
$10bobo$11b2o5$14b3o$16bo$15bo10bo$25b2o$25bobo112$112b2o$111b2o$113bo
!

That will simplify the mechanism a bit.... when a returning glider is not detected we now have just four streams that need to be killed instead of five. We can achieve this with just two gliders as opposed to three in the current design:

Code: Select all

x = 83, y = 178, rule = B3/S23
8bo$6bobo$7b2o$76bobo$76b2o$77bo2$8bo$9b2o$2bobo3b2o$3b2o$3bo52$bo$b2o
$obo110$81b2o$80b2o$82bo!

I shouldn't work on this too much more at the moment. If anyone wants to have a go it is cool with me.

EDIT: I suppose the second optimisation would apply to the current design if the Cordership and the two gliders that hit it were reflected about their line of travel... hey ho.

Re: Building a reverse caber-tosser

Posted: June 30th, 2018, 9:05 am

by dvgrn

chris_c wrote:First I found a puffer with a 7G synthesis that can reflect a single glider. The source of the puffer was this post by Saka. That should allow us to remove one of the NW travelling switch engines...

I guess it's a nice-to-have, but not strictly necessary, to find a way to send a couple of Corderships back up the puffer ash to clean up the block and boat chains, and then crash into that single leftover block off to the side without sending out any gliders.

The two Corderships will have to be created by a seed constellation, since they can't be sent on their way until after the block+boat puffer has crashed. But there's no problem adding a few freeze-dried gliders to the Cordership-making seed, to adjust that singleton block into a clean one-time two-Cordership eater... that might be just as cheap as finding a crash that sends a glider back to the origin, to trigger a final cleanup meteor shower for a messy collision.

The alternative to all of this is to do something like send Corderships, then shoot them down from behind when the right amount of time has passed -- but that will take a computationally masochistic computer-constructor design.

It seems like it will be a lot more satisfying to be able to demonstrate that seed constellations can be arranged to build Corderships that clean up all the GPSE ash, without resorting to difficult universal-computer-based simulations.

Re: Building a reverse caber-tosser

Posted: July 1st, 2018, 12:21 pm

by calcyman

chris_c wrote:I have a redesign in mind that should remove two further switch engines and take us down to 50 gliders in total.

Excellent. So even if the tubstretcher synthesis didn't exist, we'd have a completely different method of synthesising a 2017-bit still-life in no more than 50 gliders.

We can leave the GPSE-based DFIRE shotgun with 3-amortized-glider BLSE synthesis as is; the rest of the circuitry sounds like it needs modifying. I believe Extrementhusiast's glider pair reflection was the only component of the original design still present in the 58-glider solution, so once this is replaced with the single-glider reflection, we'll have completed a full iteration of the Ship of Theseus.

I wonder whether another glider or two can be shaved off by using 3-glider GPSE syntheses in locations where nearby ash will catch or suppress the spare gliders.

Re: Building a reverse caber-tosser

Posted: July 1st, 2018, 5:47 pm

by chris_c

I found some more tricks (it seems like I am unable to put this project down). First of all I used the glider + TL reaction as a cheaper way to produce the glider heading towards the puffer and liberate a PULL operation. Secondly I realised that changing the DFIRE operation so that it was independent of the PULL operation would be beneficial. Although this means there is an extra stream heading SE we save two streams elsewhere because there is no need for a U-bend in the detection mechanism.

The pattern below features 8 glider streams, a block and a Corderpuffer. As shown it produces a PULL operation but if the incoming glider is shifted by 32 cells then a DFIRE and a PULL operation are produced. We might hope that the complete pattern can be synthesised in 8 * 4 gliders for the GPSE's, 7 gliders for the Corderpuffer, 3 gliders for the BLSE and 2 gliders for the block for a total of 44 gliders.

Code: Select all

x = 878, y = 1111, rule = B3/S23
obo$b2o$bo5$3bo$bobo$2b2o23$26bo$27b2o$26b2o2$32bo$33b2o$32b2o26$64bob
o$65b2o$65bo5$67bo$65bobo$66b2o23$90bo$91b2o$90b2o2$96bo$97b2o$96b2o
26$128bobo$129b2o$129bo5$131bo$129bobo$130b2o23$154bo$155b2o$154b2o2$
160bo$161b2o$160b2o26$192bobo$193b2o$193bo5$195bo$193bobo$194b2o23$
218bo$219b2o$218b2o2$224bo$225b2o$224b2o26$256bobo$257b2o$66bo190bo$
67bo$65b3o3$259bo$257bobo$258b2o17$87bo$85bobo$86b2o$90bo$89bo$89b3o$
282bo$283b2o$282b2o2$288bo$93bo195b2o$92b2o194b2o$92bobo4$77bo$75bobo$
76b2o5$79b3o$81bo$80bo10bo$90b2o$90bobo10$320bobo$321b2o$321bo5$323bo$
321bobo$322b2o23$346bo$347b2o$346b2o2$352bo$353b2o$352b2o204$318bo$
319b2o$318b2o62$372b2o$372b2o32$325b2o$324bobo$326bo62$261b2o459b2o$
260bobo459b2o$262bo34$351bo$351b2o$350bobo25$322bo$197b2o123b2o$196bob
o122bobo231b2o$198bo356bobo$555bo33$287bo$287b2o$286bobo25$258bo$133b
2o123b2o$132bobo122bobo359b2o$134bo484bobo$619bo33$223bo$223b2o$222bob
o25$194bo$69b2o123b2o$68bobo122bobo487b2o$70bo612bobo$683bo33$159bo$
159b2o$158bobo25$130bo$5b2o123b2o$4bobo122bobo615b2o$6bo740bobo$747bo
33$95bo$95b2o$94bobo25$66bo$66b2o$65bobo743b2o$811bobo$811bo33$31bo$
31b2o$30bobo25$2bo$2b2o$bobo871b2o$875bobo$875bo!

Re: Building a reverse caber-tosser

Posted: July 2nd, 2018, 8:58 am

by chris_c

Here is a 43 glider synthesis of the above pattern showing a PULL followed by a DFIRE operation. The minimum population is 181 cells after 8192 generations. It is one glider cheaper than a slightly earlier version of this post because of an idea from dvgrn below (Thanks!):

Code: Select all

x = 7172, y = 7104, rule = B3/S23
63bo$64b2o$63b2o11$4275bo$4273b2o$4274b2o25$161bo$159bobo$160b2o$4252b
o$4251bo$4251b3o25$5333bo$5333bobo$5333b2o13$52bo$53b2o$52b2o10$222bob
o$223b2o$223bo$5312bo$5310b2o$5311b2o107$174bo$175b2o$174b2o210$227bob
o$228b2o$228bo21$248bo$249b2o$248b2o2$5231bobo$5231b2o$5232bo11$238bo$
239b2o$238b2o1949$123bo$124b2o$123b2o18$4248bobo$4248b2o$154bo4094bo$
155bo$153b3o39$185bo$183bobo$184b2o17$4310bo$4309bo$4309b3o$214bo$215b
2o$214b2o5$2198bobo$2199b2o$2199bo96$4348bo$4347bo$4347b3o1535$4255bo$
4254b2o$4254bobo36$56bo$56b2o$55bobo$4152b2o$4152bobo$4152bo18$25b3o$
27bo$26bo991$5313b3o$5313bo$5314bo98$178bo$178b2o$177bobo$5266b2o$
5266bobo$5266bo18$147b3o$149bo$148bo117$5234b2o$5234bobo$5234bo10$242b
o$242b2o$241bobo$5232b2o$5232bobo$5232bo1073$150b2o$149bobo$151bo61$
211bo$211b2o$210bobo10$2201b3o$2203bo$2202bo$6293b2o$6293bobo$6293bo
25$2179b2o$2180b2o$2179bo67$4345b2o$4344b2o$4346bo$253bo$253b2o$252bob
o25$4367b2o$4367bobo$4367bo25$3o$2bo$bo340$67bo$67b2o$66bobo$7169b2o$
7169bobo$7169bo!

Re: Building a reverse caber-tosser

Posted: July 2nd, 2018, 9:03 am

by dvgrn

chris_c wrote:We might hope that the complete pattern can be synthesised in 8 * 4 gliders for the GPSE's, 7 gliders for the Corderpuffer, 3 gliders for the BLSE and 2 gliders for the block for a total of 44 gliders.

Impressive! I'm a little sad that the strange and wonderful no-stationary-circuitry feature is gone in this design, but on the other hand, when the stationary circuitry is just a single block, that's fairly wonderful too.

Have you checked to see if a glider colliding with the pre-TL spark might just happen to produce a block in the right place, with other optional junk to the south maybe? That would save another glider, and put us almost within striking distance of... well, my original article title was "The Meaning of Life is 42 -- But the Cost of Living is Capped at 329". It's very entertaining that the Cost of Living is trending so rapidly toward the Meaning-of-Life number.

Re: Building a reverse caber-tosser

Posted: July 2nd, 2018, 9:13 am

by chris_c

dvgrn wrote: Have you checked to see if a glider colliding with the pre-TL spark might just happen to produce a block in the right place, with other optional junk to the south maybe? That would save another glider, and put us almost within striking distance of... well, my original article title was "The Meaning of Life is 42 -- But the Cost of Living is Capped at 329". It's very entertaining that the Cost of Living is trending so rapidly toward the Meaning-of-Life number.

Great idea... !

Code: Select all

x = 150, y = 68, rule = B3/S23
65b2o$64bobo16b2o$66bo16bobo$83bo24$42b2o$43b2o$42bo35$b2o$obo144b2o$
2bo144bobo$147bo!

I will update my previous post with the new total of 43!

Re: Building a reverse caber-tosser

Posted: July 2nd, 2018, 2:51 pm

by calcyman

To get even lower, it might be possible to replace the 4-glider shotgun with a 2-glider design based on the 'crystallisation and decay' reaction. This relies on the fact that 19fd (the spatial period of the crystal) is coprime with the spacing of blocks in the output of a BLSE.

Unfortunately, the other blocks in the BLSE output currently get in the way of the crystallisation:

Code: Select all

x = 187, y = 170, rule = B3/S23
15b2o$15b2o11$14b5o$13bob3obo$14bo3bo$15b3o5b2o14b2o9b2o$16bo6b2o15b2o
8b2o$36b5o$12bo23b4o$11b2o$2o8b2o4b2o8b2o8b4o$2o7b3o4b2o7bobob2o5b5o$
10b2o4b2o6b2o3b2o9b2o8b2o$11b2o12bobob2o8b2o9b2o$12bo13b2o35$91b2o$91b
2o2$85b2o$59bo25b2o$60b2o$59b2o$81b2o$81b2o16b2o$99b2o9$94b2o$94b2o3$
90b2o$90b2o$115b2o$115b2o2$109b2o$109b2o3$105b2o$105b2o16b2o$123b2o9$
118b2o$118b2o3$114b2o$114b2o$139b2o$139b2o2$133b2o$133b2o3$129b2o$129b
2o16b2o$147b2o9$142b2o$142b2o3$138b2o$138b2o$163b2o$163b2o2$157b2o$
135b2o20b2o$135b2o2$153b2o$153b2o16b2o$171b2o2$166bo$143b2o21bo$143b2o
19b3o$163b2o$162b2o$163b2o14b2o$155b2o22b2o$154b2o$155bob4o$158bo$163b
o$159bo3bo3b3o$166bo2bo$170bo$166b2o$166b2o3bo$171bo12bo$159b2o8bo12b
3o$159b2o6b3o11b2ob2o$167b2o$167bo13b2o$182bo$182b2o$167b3o13bo$182b3o
$182b3obo$186bo$186bo!

...but it might be possible to use the DFIRE glider to clear those annoying extra blocks.

In the worst-case scenario, DFIRE/CLEAN might need to be a glider pair rather than a single glider. But then we still only need a 3- instead of 4-GPSE shotgun.

Thoughts?

Re: Building a reverse caber-tosser

Posted: July 2nd, 2018, 3:12 pm

by calcyman

It transpires only one orbit of blocks interfere with the crystal growth, so we should have lots (6?) of lanes for potential DFIRE gliders:

Code: Select all

x = 131, y = 129, rule = LifeHistory

22.2A$22.2A2$16.2A$16.2A4$30.2A$30.2A4$B$2B$3B$4B$.4B$2.4B12.D6.2A$3.

4B12.D5.2A$4.4B12.D$5.4B12.D$6.4B12.D$7.4B6.5B.D$8.4B2.10BD21.2A$9.

17B20.2A$10.17B$11.17B12.2A$12.17B11.2A$10.20B$9.21BD$10.19B2.D4.2A$

9.18B5.D3.2A16.2A$9.5B2A13B4.D20.2A$10.4B2A15B3.D$10.21B4.D$12.20B4.D

$16.16B5.D$18.11B2AB6.D$18.10BA2BAB6.D$19.10B2A2B7.D$18.15B8.D$18.7BA

9B.5B.D6.2A$18.6BABA16BD5.2A$18.6BABA18B$18.7BA20B$19.28B$19.29B$20.

18B2A9B21.2A$20.17BA2BA8BD20.2A$21.17B2A8B2.D$22.5B.18B5.D12.2A$23.4B

.6BA13B4.D11.2A$24.2B3.4BABA14B3.D$29.4BABA14B4.D$31.3BA16B4.D4.2A$

34.17B5.D3.2A16.2A$37.11B2AB6.D20.2A$37.10BA2BAB6.D$38.10B2A2B7.D$37.

15B8.D$37.7BA9B.5B.D$37.6BABA16BD$37.6BABA18B$37.7BA20B$38.28B$38.29B

6.2A$39.18B2A9B5.2A$39.17BA2BA8BD$40.17B2A8B2.D$41.5B.18B5.D$42.4B.6B

A11B6.D$43.2B3.4BABA10B7.D21.2A$48.4BABA11B7.D20.2A$50.3BA12B8.D$53.

15B7.D12.2A$56.11B2AB6.D11.2A$56.10BA2BAB6.D$57.10B2AB8.D$59.9B11.D4.

2A$61.2BA2B14.D3.2A9.4B3.2A$61.BABAB15.D13.5B2.2A$62.ABA17.D11.6B$62.

BAB18.D10.6B$63.B10.2A8.D10.5B8.B$74.2A9.D5.9B7.3B$86.D3.9B8.3B$82.5B

D2.11B6.5B$82.5B.D12B4.8B$79.10BD2.10B3.8B$78.12BD.5B2A3B3.8B$79.12BD

5B2A4B2.10B$81.10B.D11B.11B$81.2B2.2B5.BD11B2.9B$90.B.B2C10B.12B$93.

2C24B$92.26B2A$93.25B2A$94.25B$97.15B2A4B$90.2A3.17B2A4B.B$90.2A2.30B

$95.31B$95.13B2A17B$95.13B2A16B2A$95.31B2A$96.5B3.23B$96.5B3.22B$97.B

2AB2.23B.B$98.2A2.29B$103.28B$103.28B$103.28B$103.28B$102.19B2A8B$

103.18B2A8B$105.26B$105.26B$106.11B2C12B$109.8B2C12B$109.22B$110.21B$

112.19B$112.19B$113.B2AB2.12B$114.2A2.13B$119.12B$119.12B$119.12B!

Now to see whether any of them work...

Re: Building a reverse caber-tosser

Posted: July 2nd, 2018, 3:35 pm

by dani

If I'm reading this all right, we can now synthesize anything that i̶s̶n̶'̶t̶ ̶a̶ ̶G̶o̶E̶ can be constructed using any amount of gliders in 43 gliders? This is amazing! Wonderful job to adam, chris, dave, saka, goldtiger, and everyone else! Even if I'm still a bit unclear on the whole thing...I could run some corderpuffer searches or write some scripts if necessary..

EDIT: sorry...

Re: Building a reverse caber-tosser

Posted: July 2nd, 2018, 3:39 pm

by Macbi

danny wrote:anything that isn't a GoE in 43 gliders

Anything that can be synthesised by gliders can be synthesised with 43 gliders. We don't know if every non-GoE is glider constructable.

Re: Building a reverse caber-tosser

Posted: July 2nd, 2018, 7:52 pm

by Sokwe

Macbi wrote:
danny wrote:anything that isn't a GoE in 43 gliders
Anything that can be synthesised by gliders can be synthesised with 43 gliders. We don't know if every non-GoE is glider constructable.

There are a few known patterns that are not Gardens of Eden but are also not glider constructible (see grandfather problem).

Re: Building a reverse caber-tosser

Posted: July 2nd, 2018, 10:01 pm

by chris_c

calcyman wrote:To get even lower, it might be possible to replace the 4-glider shotgun with a 2-glider design based on the 'crystallisation and decay' reaction. This relies on the fact that 19fd (the spatial period of the crystal) is coprime with the spacing of blocks in the output of a BLSE.

Unfortunately, the other blocks in the BLSE output currently get in the way of the crystallisation:
Code: Select all
x = 187, y = 170, rule = B3/S23
15b2o$15b2o11$14b5o$13bob3obo$14bo3bo$15b3o5b2o14b2o9b2o$16bo6b2o15b2o
8b2o$36b5o$12bo23b4o$11b2o$2o8b2o4b2o8b2o8b4o$2o7b3o4b2o7bobob2o5b5o$
10b2o4b2o6b2o3b2o9b2o8b2o$11b2o12bobob2o8b2o9b2o$12bo13b2o35$91b2o$91b
2o2$85b2o$59bo25b2o$60b2o$59b2o$81b2o$81b2o16b2o$99b2o9$94b2o$94b2o3$
90b2o$90b2o$115b2o$115b2o2$109b2o$109b2o3$105b2o$105b2o16b2o$123b2o9$
118b2o$118b2o3$114b2o$114b2o$139b2o$139b2o2$133b2o$133b2o3$129b2o$129b
2o16b2o$147b2o9$142b2o$142b2o3$138b2o$138b2o$163b2o$163b2o2$157b2o$
135b2o20b2o$135b2o2$153b2o$153b2o16b2o$171b2o2$166bo$143b2o21bo$143b2o
19b3o$163b2o$162b2o$163b2o14b2o$155b2o22b2o$154b2o$155bob4o$158bo$163b
o$159bo3bo3b3o$166bo2bo$170bo$166b2o$166b2o3bo$171bo12bo$159b2o8bo12b
3o$159b2o6b3o11b2ob2o$167b2o$167bo13b2o$182bo$182b2o$167b3o13bo$182b3o
$182b3obo$186bo$186bo!
...but it might be possible to use the DFIRE glider to clear those annoying extra blocks.

In the worst-case scenario, DFIRE/CLEAN might need to be a glider pair rather than a single glider. But then we still only need a 3- instead of 4-GPSE shotgun.

Thoughts?

Interesting. The crystal you show in the above pattern lasts for a few dozen iterations at least. More concerning is that a crystal starting from the other block in the BLSE runs into almost immediate doom:

Code: Select all

x = 33, y = 38, rule = B3/S23
23b2o$23b2o2$17b2o$17b2o3$13b2o$13b2o16b2o$31b2o4$bo$2bo$3o3$26b2o$26b
2o3$22b2o$22b2o5$16bo$17bo$15b3o6$27b2o$27b2o!

I only found two DFIRE operations on a block and neither is suitable for killing the annoying block:

Code: Select all

x = 65, y = 14, rule = B3/S23
obo49bo$b2o47bobo$bo49b2o2$58bo$56bobo$57b2o$63b2o$5bo57b2o$3bobo$4b2o
2$10b2o$10b2o!

So next I looked at DFIRE operations on half of a honey farm. This is the one I had most success with (by coincidence one of the gliders is on the same lane as the crystal glider):

Code: Select all

x = 21, y = 13, rule = B3/S23
o6bobo$b2o5b2o$2o6bo3$19bo$18bobo$18bobo$19bo2$14b2o$13bo2bo$14b2o!

It is also capable of doing a couple of other alterations to a crystal. The first leaves us with a block in honey-farm position that we would not have got for around 15 more iterations. The other kills off the crystal growing phase and puts us back into decay mode.

Code: Select all

x = 108, y = 33, rule = B3/S23
o6bobo$b2o5b2o$2o6bo9$78bo6bobo$79b2o5b2o$78b2o6bo4$26b2o$17b2o6bobo$
17b2o6b2o$93bo$92bobo$24b2o66bobo$24b2o67bo2$37b2o66b2o$36bo2bo64bo2bo
$37b2o66b2o2$33bo67bo$32bobo65bobo$32bobo65bobo$33bo67bo!

Now the DFIRE operation does not operate properly at the first time of asking, but at least it doesn't crash the entire pattern. Luckily if we throw in another DFIRE operation 20 iterations later then everything just works:

Code: Select all

x = 3817, y = 3813, rule = B3/S23
15b2o$15b2o7$16bo$15b3o$14b5o$13bobobobo$13b2o3b2o2$39b4o$16bo6b2o14bo
2b2o6b2o$15bobo5b2o15bo2b2o5b2o$15bobo22bo2bo$10bobo3bo24b2o$9bo2bo3b
2o7bo3bo$2o6b2o6b2o6bobobobo10b2o$2o4b2o3bo3bo2bo3b2o2bobo2b2o7bo2bo$
8b2o6b2o4b2o7b2o7bo2b2o5b2o$9bo2bo9b2o2bobo2b2o6bo2b2o6b2o$10bobo11bob
obobo8b4o$25bo3bo40$53bo6bobo$54b2o5b2o$53b2o6bo170$233bo$234b2o$233b
2o171$405bobo$406b2o$406bo170$578bo$579b2o$578b2o171$750bobo$751b2o$
751bo170$923bo$924b2o$923b2o171$1095bobo$1096b2o$1096bo170$1268bo$
1269b2o$1268b2o171$1440bobo$1441b2o$1441bo170$1613bo$1614b2o$1613b2o
171$1785bobo$1786b2o$1786bo170$1958bo$1959b2o$1958b2o171$2130bobo$
2131b2o$2131bo170$2303bo$2304b2o$2303b2o171$2475bobo$2476b2o$2476bo
170$2648bo$2649b2o$2648b2o171$2820bobo$2821b2o$2821bo170$2993bo$2994b
2o$2993b2o171$3165bobo$3166b2o$3166bo170$3338bo$3339b2o$3338b2o171$
3503bo6bobo$3504b2o5b2o$3503b2o6bo162$3711b2o$3711b2o2$3705b2o$3705b2o
3$3701b2o$3683bo17b2o16b2o$3684b2o33b2o$3683b2o8$3714b2o$3714b2o5$
3735b2o$3735b2o2$3729b2o$3729b2o3$3725b2o$3725b2o16b2o$3743b2o9$3738b
2o$3738b2o5$3759b2o$3759b2o2$3753b2o$3753b2o3$3749b2o$3749b2o16b2o$
3767b2o9$3762b2o$3762b2o3$3758b2o$3758b2o$3783b2o$3783b2o2$3777b2o$
3777b2o3$3773b2o$3773b2o16b2o$3791b2o3$3763b2o$3763b2o5$3786b2o$3786b
2o3$3782b2o$3782b2o$3807b2o$3807b2o2$3801b2o$3779b2o20b2o$3779b2o2$
3797b2o$3797b2o16b2o$3815b2o3$3787b2o$3787b2o5$3810b2o$3810b2o3$3806b
2o$3806b2o5$3803b2o$3803b2o7$3811b2o$3811b2o!

This should make it relatively easy to use a 3 glider shotgun and remove one of the switch engines in the latest design. You could also make a 2 glider shotgun version where the PULL and DFIRE operations are dependent but I think this will cost more in "circuitry" than it saves.

One of the blocks being so close to doom shaped my approach to this problem significantly. Does anyone see another way around it?

EDIT: Ha, just moving the BLSE so that the glider hits the block in block-pull position makes things a lot simpler. It doesn't solve the problem that the crystal is close to doom in that location though.

Code: Select all

x = 194, y = 177, rule = B3/S23
o6bobo$b2o5b2o$2o6bo30$40bo$41b2o$40b2o9$88b2o$88b2o2$82b2o$82b2o3$78b
2o$78b2o16b2o$60bo35b2o$61b2o$60b2o7$91b2o$91b2o5$112b2o$112b2o2$106b
2o$106b2o3$102b2o$102b2o16b2o$120b2o9$115b2o$115b2o5$136b2o$136b2o2$
130b2o$130b2o3$126b2o$126b2o16b2o$144b2o9$139b2o$139b2o3$135b2o$135b2o
$160b2o$160b2o2$154b2o$154b2o3$150b2o$150b2o16b2o$168b2o3$140b2o$140b
2o5$163b2o$163b2o3$159b2o$159b2o$184b2o$184b2o2$178b2o$156b2o20b2o$
156b2o2$174b2o$174b2o16b2o$192b2o3$164b2o$164b2o5$187b2o$187b2o3$183b
2o$183b2o5$180b2o$180b2o7$188b2o$188b2o!

Re: Building a reverse caber-tosser

Posted: July 3rd, 2018, 3:23 am

by Macbi

Sokwe wrote:
Macbi wrote:
danny wrote:anything that isn't a GoE in 43 gliders
Anything that can be synthesised by gliders can be synthesised with 43 gliders. We don't know if every non-GoE is glider constructable.
There are a few known patterns that are not Gardens of Eden but are also not glider constructible (see grandfather problem).

You're right of course.

Perhaps a new bit of nomenclature is needed? We could call a pattern "native" if it has an infinite chain of ancestors each with finite population. Then every glider constructable pattern would be native, so the obvious conjecture would be that every native pattern was glider constructable.

Personally I suspect this is false, and that there even exists a still life that isn't glider constructable.

EDIT: On second thoughts "native" sounds kind of stupid. I was originally thinking "natural", but that already has a meaning.

Re: Building a reverse caber-tosser

Posted: July 3rd, 2018, 7:55 am

by Gamedziner

How would one go about turning this into a true replicator?

Re: Building a reverse caber-tosser

Posted: July 3rd, 2018, 8:22 am

by dvgrn

Gamedziner wrote:How would one go about turning this into a true replicator?

One would engage in a handwaving exercise, describing structures and mechanisms that are practically impossible to build as any kind of working models.

And by "practically impossible", I really do mean "impossible in practice". Calculating the positions of 43-or-whatever gliders that constitute a quadratic growth replicator does not seem like a task that can actually be completed by humans.

Re: Building a reverse caber-tosser

Posted: July 3rd, 2018, 8:47 am

by calcyman

chris_c wrote:This should make it relatively easy to use a 3 glider shotgun and remove one of the switch engines in the latest design. You could also make a 2 glider shotgun version where the PULL and DFIRE operations are dependent but I think this will cost more in "circuitry" than it saves.

Excellent -- so there should be no difficulty getting down to 40, or possibly 39 if we can continue to save a glider in the BLSE synthesis. This is only a factor of two larger than itaibn's target:

itaibn wrote:Congratulations on 329 glider universal constructor! Now let's see if we can do it in under 20 gliders.

I don't think this is as ridiculous as it sounds. Look at how low the population for a quadratic growth pattern got, compared to the population of the first breeder. It seems likely to me that some Nick-Gotts-style pattern of carefully interacting switch engine puffers could also exhibit universal construction at a lower glider-count or starting population.

...which is frighteningly predictive of what we proceeded to do: replace the guns with GPSEs and progressively simplify. It's not exactly Gottsian just yet, but it's close.

Perhaps before explicitly building the 39/40-glider solution, it would be helpful to perform an intensive search to see whether there's a single-glider replacement of the crystal-to-glider operation -- or, even before that, verifying the truth value of the italic think. That could lead to a 35/36-glider solution, beyond which we'll need new conceptual developments.

Gamedziner wrote:How would one go about turning this into a true replicator?

By firstly trying the more attainable goal of building a single pulsar.

Re: Building a reverse caber-tosser

Posted: July 4th, 2018, 7:31 am

by itaibn

dvgrn wrote:
Gamedziner wrote:How would one go about turning this into a true replicator?
One would engage in a handwaving exercise, describing structures and mechanisms that are practically impossible to build as any kind of working models.

And by "practically impossible", I really do mean "impossible in practice". Calculating the positions of 43-or-whatever gliders that constitute a quadratic growth replicator does not seem like a task that can actually be completed by humans.

I find your lack of faith in the human spirit naive. Not a task that can be completed by humans? First, let's remember that designing patterns in the Game of Life is mainly done by a small number of hobbyists in their spare time. I hope that hasn't distorted your judgment of what things are humanly possible when people make a serious effort. Compare the complexity of GoL designs with that of integrated circuits, or practically anything built in the real world. If the Game of Life were not just a game but a 10^8 dollar industry I imagine we'd have Verilog-to-Life compilers or similar CAD tools, and programs that can design a glider synthesis for any constellation or spaceship flotilla made up of glider-constructable parts, creates a Spartan still-life seed for that glider synthesis, and a slow-salvo synthesis which creates and activates that seed, and many people working full-time to handle these programs. Do you think in such an environment people will have any difficulty creating a self-replicator based on a 43-or-less universal glider constructor? I'd say that this is easily within human possibility

With the current hobbyist level of effort I still won't be surprised if such a self-replicator someday gets built. We know how such a thing could be built in principle, and it takes a lot of time and effort to actually build such a thing with current technology, but I don't think it's more than what a single person can do working continuously on it for ten years.

Anyways, I hope you guys are not too annoyed by all my dreaming and high expectations while everyone else is doing all the real work. I'll add a more constructive remark: The way these designs work is that the displacement between gliders encodes in binary the design of a pattern. How much quicker would a reaction to make a particular pattern be if there were more gliders than the minimum necessary? Well, the most efficient use of an addition glider is not to simplify the mechanism, but rather to use the displacement of this glider as a source of additional bits. Similarly, in the current design, the exact distances between the switch engine puffers is irrelevant as long as they're far enough. Thus their distance can be used as a source of additional bits. One possible mechanism for this is that the first reverse caber-tosser builds components of a pattern, then launches a glider stream which reacts with starting point of one of the switch engines and creates a second reverse caber-tosser pattern to complete the pattern. If the starting position of each switch engine could be varied independently this would be a rather large source of additional bits per log-time, but it looks like the current design depends to a certain extent on the first gliders of all the glider streams coming to the intersection point simultaneously. Another displacement that could potentially be used for additional bits is the distance between the intersection points of the glider streams and the block-producing switch engine.

Re: Building a reverse caber-tosser

Posted: July 4th, 2018, 10:09 am

by dvgrn

itaibn wrote:
dvgrn wrote:Calculating the positions of 43-or-whatever gliders that constitute a quadratic growth replicator does not seem like a task that can actually be completed by humans.
If the Game of Life were not just a game but a 10^8 dollar industry I imagine we'd have Verilog-to-Life compilers or similar CAD tools, and programs that can design a glider synthesis for any constellation or spaceship flotilla made up of glider-constructable parts, creates a Spartan still-life seed for that glider synthesis, and a slow-salvo synthesis which creates and activates that seed, and many people working full-time to handle these programs. Do you think in such an environment people will have any difficulty creating a self-replicator based on a 43-or-less universal glider constructor?

Yup, that's exactly what I think. 10^8 dollars is an insignificant fraction of what you'd have to throw at this particular problem to solve it completely.

itaibn wrote:I'd say that this is easily within human possibility...I don't think it's more than what a single person can do working continuously on it for ten years...

Seems to me that that estimate is off by quite a few orders of magnitude. Some of my previous posts give an indication of why I think so.

The key detail is that there have been two very different types of 43-glider patterns discussed here.
A 43-glider pattern that builds a pulsar (or other small object) and nothing else, might well be within your ten-person-year budget. A replicator, or the more or less equivalent Yottabyte Universal Constructor Knightship described in the above link, seems to be many orders of magnitude removed from that. It's so much harder that my guess would be that humans will have evolved into something else before the job is done.

-- I actually chose the "completed by humans" phrase on purpose because of that evolutionary limitation. Was going to add another sentence about that, but then decided to keep things shorter for a change. (!)

Try making just a rough estimate of the number of bits needed to implement any kind of BABC universal constructor design, where you use some bits to build a structure to store a ridiculous number of additional bits... then you store those bits... and then you use those bits, not only to clean up the huge mess already created, but to create 86 new gliders at exactly the right distance away. (If we only built 43 new gliders, we'd have at best a spaceship, not a replicator.)

Some of those gliders have to be placed at a very precise 2^[colossal-number-of-bits] distance. This is not an easy Conway's Life engineering problem, to say the least.

Now, imagine representing the positions of the required 43 initial gliders in the most compact possible form. If you can do it in less than a brontobyte, I'll be surprised.

Okay, then assume that humans have built the necessary data storage to hold that brontobyte of information, and are motivated to waste their time maintaining it. Seems like a big assumption, but let's go with it.

Next we need an estimate of the time required to simulate those 43 gliders and make sure there aren't any bugs in the design. The storage requirements for a lot of the intermediate states of this pattern are much bigger than for just the initial state, so our hypothetical humans are going to need to build more storage. I suspect we'll either run out of planet, or run out of sunshine, somewhere in there. I'm not ruling out moving to a different solar system to complete this project, but I'd say the odds are very good we'll have evolved beyond Homo sapiens sapiens by then.

itaibn wrote:How much quicker would a reaction to make a particular pattern be if there were more gliders than the minimum necessary? Well, the most efficient use of an addition glider is not to simplify the mechanism, but rather to use the displacement of this glider as a source of additional bits.

Yeah, as soon as you're allowed to go above the absolute minimum number of gliders, things get a lot easier. But there start to be so many options for improvement that it's hard to decide which one to choose. It's kind of a nice feature of the absolute-minimum-gliders design, that the resulting N-glider patterns are not buildable in practice.

Re: Building a reverse caber-tosser

Posted: July 5th, 2018, 11:53 am

by chris_c

I wrote this:

chris_c wrote: Ha, just moving the BLSE so that the glider hits the block in block-pull position makes things a lot simpler. It doesn't solve the problem that the crystal is close to doom in that location though.

But the second sentence is just wrong. I can't remember if I just made a mistake or didn't bother to analyse the subsequent debris properly. Although the growth of the crystal is disturbed by the "annoying" block, the debris that is left behind is in the perfect location for making two crystals. Therefore my idea was to use the first crystal to deposit some debris and then the second to crash into it and produce a glider... and it worked! Just two slow gliders seven lanes away from the main stream of gliders is enough to produce a FIRE operation:

Code: Select all

x = 1992, y = 1983, rule = LifeHistory
.A$2.A$3A30$33.A$34.A$32.3A30$65.A$66.A$64.3A30$97.A$98.A$96.3A30$
129.A$130.A$128.3A30$161.A$162.A$160.3A30$193.A$194.A$192.3A30$225.A$
226.A$224.3A30$257.A$258.A$256.3A30$289.A$290.A$288.3A30$321.A$322.A$
320.3A30$353.A$354.A$352.3A30$385.A$386.A$384.3A30$417.A$418.A$416.3A
30$449.A$450.A$448.3A30$481.A$482.A$480.3A30$513.A$514.A$512.3A30$
545.A$546.A$544.3A30$577.A$578.A$576.3A30$609.A$610.A$608.3A30$641.A$
642.A$640.3A30$673.A$674.A$672.3A30$705.A$706.A$704.3A30$737.A$738.A$
736.3A30$769.A$770.A$768.3A30$808.A$809.A$807.3A30$833.A$834.A$832.3A
30$865.A$866.A$864.3A30$897.A$898.A$896.3A30$929.A$930.A$928.3A30$
961.A$962.A$960.3A30$993.A$994.A$992.3A30$1025.A$1026.A$1024.3A30$
1057.A$1058.A$1056.3A30$1089.A$1090.A$1088.3A30$1121.A$1122.A$1120.3A
30$1153.A$1154.A$1152.3A30$1185.A$1186.A$1184.3A30$1224.A$1225.A$
1223.3A30$1249.A$1250.A$1248.3A30$1281.A$1282.A$1280.3A30$1313.A$
1314.A$1312.3A30$1345.A$1346.A$1344.3A30$1377.A$1378.A$1376.3A30$
1409.A$1410.A$1408.3A30$1441.A$1442.A$1440.3A30$1473.A$1474.A$1472.3A
30$1505.A$1506.A$1504.3A30$1537.A$1538.A$1536.3A30$1569.A$1570.A$
1568.3A30$1601.A$1602.A$1600.3A30$1633.A$1634.A$1632.3A30$1665.A$
1666.A$1664.3A30$1697.A$1698.A$1696.3A30$1729.A$1730.A$1728.3A30$
1761.A$1762.A$1760.3A30$1793.A$1794.A$1792.3A30$1825.A$1826.A$1824.3A
23$1886.2A$1886.2A2$1880.2A$1880.2A3$1857.A18.2A$1858.A17.2A16.2A$
1856.3A35.2A9$1889.2A$1889.2A5$1910.2A$1910.2A2$1904.2A$1904.2A3$
1900.2A$1900.2A16.2A$1918.2A6$1889.A$1890.A$1888.3A$1913.2A$1913.2A5$
1934.2A$1934.2A2$1928.2A$1928.2A3$1924.2A$1924.2A16.2A$1942.2A9$1937.
2A$1937.2A3$1933.2A$1933.2A$1958.2A$1958.2A2$1952.2A$1952.2A3$1948.2A
$1948.2A16.2A$1966.2A3$1938.2A$1938.2A5$1961.2A$1961.2A3$1957.2A$
1957.2A$1982.2A$1982.2A2$1976.2A$1954.2A20.2A$1954.2A2$1972.2A$1972.
2A16.2A$1990.2A3$1962.2A$1962.2A5$1985.2A$1985.2A3$1981.2A$1981.2A5$
1978.2A$1978.2A7$1986.2A$1986.2A!
[[ ZOOM 3 STEP 16 X 930 Y 930 ]]

Lurking in the pattern you will see that firing along the second glider lane at the appropriate time causes the crystal to advance by 9fd instead of 19fd. Since these values are coprime we can use these operations to grow both of the intermediate crystals by any sufficiently large distance and so it looks like we can make a universal constructor in just 36 or 37 gliders (depending on whether the BLSE will cost 3 or 4).

Re: Building a reverse caber-tosser

Posted: July 5th, 2018, 12:05 pm

by dvgrn

chris_c wrote:Lurking in the pattern you will see that firing along the second glider lane at the appropriate time causes the crystal to advance by 9fd instead of 19fd. Since these values are coprime we can use these operations to grow both of the intermediate crystals by any sufficiently large distance and so it looks like we can make a universal constructor in just 36 or 37 gliders (depending on whether the BLSE will cost 3 or 4).

I was going to ask a few days ago, but didn't have time to look into it very far. Still haven't had time, but I'll ask anyway:

Might there be a way to also use the second stream to generate a new elbow block from a partly grown crystal, removing the need for the BLSE as a source of elbows?

It looks to me like this wouldn't quite work, because other blocks from the BLSE ash are also needed to make everything work. Maybe it could be made to work with three glider streams, but not with two. (?)

We will need to add a glider to the new recipe to create a target for the monochromatic output gliders, right? When the DFIRE gliders were heading NE, there was some junk sitting around from BLSE construction that could be used as a target, but I don't think there will be anything extra lying around in the SW.

Re: Building a reverse caber-tosser

Posted: July 5th, 2018, 2:36 pm

by calcyman

dvgrn wrote:It looks to me like this wouldn't quite work, because other blocks from the BLSE ash are also needed to make everything work. Maybe it could be made to work with three glider streams, but not with two. (?)

We will need to add a glider to the new recipe to create a target for the monochromatic output gliders, right? When the DFIRE gliders were heading NE, there was some junk sitting around from BLSE construction that could be used as a target, but I don't think there will be anything extra lying around in the SW.

Hakuna Matata: the crystal is glide-reflective, so you can make the other stream 7hd lower (instead of higher) than the main stream and get the gliders pointing in the more conventional direction:

Code: Select all

x = 2824, y = 2815, rule = LifeHistory
.A$2.A$3A30$33.A$34.A$32.3A30$65.A$66.A$64.3A30$97.A$98.A$96.3A30$
129.A$130.A$128.3A30$161.A$162.A$160.3A30$193.A$194.A$192.3A30$225.A$
226.A$224.3A30$257.A$258.A$256.3A30$289.A$290.A$288.3A30$321.A$322.A$
320.3A30$353.A$354.A$352.3A30$385.A$386.A$384.3A30$417.A$418.A$416.3A
30$449.A$450.A$448.3A30$481.A$482.A$480.3A30$513.A$514.A$512.3A30$
545.A$546.A$544.3A30$577.A$578.A$576.3A30$609.A$610.A$608.3A30$641.A$
642.A$640.3A30$673.A$674.A$672.3A30$705.A$706.A$704.3A30$737.A$738.A$
736.3A30$769.A$770.A$768.3A30$801.A$802.A$800.3A30$833.A$834.A$832.3A
37$865.A$866.A$864.3A23$897.A$898.A$896.3A30$929.A$930.A$928.3A30$
961.A$962.A$960.3A30$993.A$994.A$992.3A30$1025.A$1026.A$1024.3A30$
1057.A$1058.A$1056.3A30$1089.A$1090.A$1088.3A30$1121.A$1122.A$1120.3A
30$1153.A$1154.A$1152.3A30$1185.A$1186.A$1184.3A30$1217.A$1218.A$
1216.3A30$1249.A$1250.A$1248.3A30$1281.A$1282.A$1280.3A30$1313.A$
1314.A$1312.3A30$1345.A$1346.A$1344.3A30$1377.A$1378.A$1376.3A30$
1409.A$1410.A$1408.3A30$1441.A$1442.A$1440.3A30$1473.A$1474.A$1472.3A
30$1505.A$1506.A$1504.3A30$1537.A$1538.A$1536.3A30$1569.A$1570.A$
1568.3A30$1601.A$1602.A$1600.3A30$1633.A$1634.A$1632.3A30$1665.A$
1666.A$1664.3A37$1697.A$1698.A$1696.3A23$1729.A$1730.A$1728.3A30$
1761.A$1762.A$1760.3A30$1793.A$1794.A$1792.3A30$1825.A$1826.A$1824.3A
30$1857.A$1858.A$1856.3A30$1889.A$1890.A$1888.3A30$1921.A$1922.A$
1920.3A30$1953.A$1954.A$1952.3A30$1985.A$1986.A$1984.3A30$2017.A$
2018.A$2016.3A30$2049.A$2050.A$2048.3A30$2081.A$2082.A$2080.3A30$
2113.A$2114.A$2112.3A30$2145.A$2146.A$2144.3A30$2177.A$2178.A$2176.3A
30$2209.A$2210.A$2208.3A30$2241.A$2242.A$2240.3A30$2273.A$2274.A$
2272.3A30$2305.A$2306.A$2304.3A30$2337.A$2338.A$2336.3A30$2369.A$
2370.A$2368.3A30$2401.A$2402.A$2400.3A30$2433.A$2434.A$2432.3A30$
2465.A$2466.A$2464.3A30$2497.A$2498.A$2496.3A30$2529.A$2530.A$2528.3A
30$2561.A$2562.A$2560.3A30$2593.A$2594.A$2592.3A30$2625.A$2626.A$
2624.3A30$2657.A$2658.A$2656.3A23$2718.2A$2718.2A2$2712.2A$2712.2A3$
2689.A18.2A$2690.A17.2A16.2A$2688.3A35.2A9$2721.2A$2721.2A5$2742.2A$
2742.2A2$2736.2A$2736.2A3$2732.2A$2732.2A16.2A$2750.2A6$2721.A$2722.A
$2720.3A$2745.2A$2745.2A5$2766.2A$2766.2A2$2760.2A$2760.2A3$2756.2A$
2756.2A16.2A$2774.2A9$2769.2A$2769.2A3$2765.2A$2765.2A$2790.2A$2790.
2A2$2784.2A$2784.2A3$2780.2A$2780.2A16.2A$2798.2A3$2770.2A$2770.2A5$
2793.2A$2793.2A3$2789.2A$2789.2A$2814.2A$2814.2A2$2808.2A$2786.2A20.
2A$2786.2A2$2804.2A$2804.2A16.2A$2822.2A3$2794.2A$2794.2A5$2817.2A$
2817.2A3$2813.2A$2813.2A5$2810.2A$2810.2A7$2818.2A$2818.2A!

EDIT: Wait, Chris, what do we do with the other block (of the pair produced by the BLSE on the target lane each period)? Oh, never mind, we can destroy it cleanly:

Code: Select all

x = 152, y = 149, rule = LifeHistory
$B$2B$3B$4B$.4B$2.4B35.2A$3.3BA34.2A$4.3BA$5.3AB26.2A$6.4B25.2A$7.4B$
8.4B$9.4B18.2A$10.4B17.2A16.2A$11.4B34.2A$12.4B$13.4B$14.4B$15.4B$16.
4B$17.4B$18.4B$19.4B$20.4B20.2A$21.4B19.2A$22.4B$23.4B$24.4B$25.4B$
26.4B35.2A$27.4B34.2A$28.4B$29.4B26.2A$30.4B25.2A$31.4B$32.4B$33.4B
18.2A$34.4B17.2A16.2A$35.3BA34.2A$36.3BA$37.3AB$38.4B$39.4B$40.4B$41.
4B$42.4B$43.4B$44.4B20.2A$45.4B19.2A$46.4B$47.4B$48.4B$49.4B$50.4B35.
2A$51.4B34.2A$52.4B$53.4B26.2A$54.4B25.2A$55.4B$56.4B$57.4B18.2A$58.
4B17.2A16.2A$59.4B34.2A$53.4B$54.4B$55.4B$56.4B$57.4B$58.4B$59.4B$60.
3BA$61.3BA27.2A$62.3AB26.2A$63.3B7.B$64.2B7.2B$65.B7.3B$73.4B$74.4B
35.2A$75.4B34.2A$76.4B$77.4B26.2A$78.4B25.2A$79.4B$80.4B$81.4B18.2A$
82.4B17.2A16.2A$83.4B34.2A$84.4B$85.4B$86.4B6.5B$87.4B2.10B$88.17B$
89.17B$90.17B$91.17B$89.20B7.2A$88.21B7.2A$89.19B$88.18B$88.18B6.2A$
89.17B6.2A$89.5B2A11B30.2A$91.3B2A11B30.2A$95.14B$97.11B2AB20.2A$97.
10BA2BAB19.2A$98.10B2AB$100.10B$102.2BA4B18.2A$102.BABA3B18.2A16.2A$
103.ABA39.2A$103.BAB$104.B$117.2A$117.2A5$140.2A$140.2A3$136.2A$136.
2A5$133.2A$133.2A7$141.2A$141.2A!

Re: Building a reverse caber-tosser

Posted: July 5th, 2018, 4:35 pm

by calcyman

We can synthesise the BLSE with three gliders:

Code: Select all

x = 324, y = 307, rule = LifeHistory
2.A$A.A$.2A62$66.A$64.A.A$65.2A62$130.A$128.A.A$129.2A62$194.A$192.A.
A$193.2A12$228.C.C$229.2C$229.C$320.C$318.2C$319.2C93$321.3C$321.C$
322.C!

This should be 35 gliders in total: 24 for the GPSEs, 3 for the BLSE, 7 for the Sakapuffer, and 1 for the block.

Also, this will be far more elegant than before because we can synthesise all the GPSEs at roughly the same time instead of having one GPSE crashing into the back of another.

Re: Building a reverse caber-tosser

Posted: July 5th, 2018, 7:36 pm

by chris_c

calcyman wrote:We can synthesise the BLSE with three gliders.

This should be 35 gliders in total: 24 for the GPSEs, 3 for the BLSE, 7 for the Sakapuffer, and 1 for the block.

Excellent. Thanks for finding that and for clarifying those other issues. The 35 glider synthesis was pretty easy to obtain from the 43 glider version. Just 6 GPSE's now and the minimum population is 143 after 5000 generations:

Code: Select all

x = 2883, y = 2768, rule = B3/S23
120bo$121b2o$120b2o2$2877bobo$2877b2o$2878bo80$306bo$305bo$305b3o26$
285b2o$284b3o$285b2o$287bo$287bo$287bo36$174bo$173bo$174bob2o$175b3o$
176b2o18$145b3o$147bo$146bo187$227bobo$228b2o$228bo21$248bo$249b2o$
248b2o2$623bobo$623b2o$624bo11$238bo$239b2o$238b2o364$626b2o$626bobo$
626bo10$242bo$242b2o$241bobo$624b2o$624bobo$624bo1568$123bo$124b2o$
123b2o17$154bo$151b4o$150bo3bo2$150b3o40$185bo$183bobo$184b2o18$214b3o
$211b3o$211b3o$212bo5$2199bo$2198bobo2$2198bo2bo$2200b2o$2201bo26$
2179b2o$2180b2o$2179bo67$251b3o$251b3o$252bo$249bobo$250bo26$271b2o$
271bobo$271bo25$3o$2bo$bo158$2880b2o$2880bobo$2880bo!

With the new mechanism it is somewhat challenging to even show an example pattern that produces a single sideways glider.