Thread for advanced questions

[vilc]

There is a 177-bit still life that can fit inside Karel's p177. I didn't check optimality; can anyone find a bigger still life that fits?

A 180-cell solution found using the symmetry constraint "-s C4" with the above LLS input file. Still no proof of optimality.

Code: Select all

x = 62, y = 62, rule = LifeHistory
25.4B4.4B$25.12B$18.3B3.14B3.3B$15.32B$14.34B$13.36B$13.36B$12.38B$
11.11B3A12B3A11B$12.9BA3BA10BA3BA9B$12.8BA20BA8B$8.B3.38B3.B$7.5B.8BA
BA14BABA8B.5B$5.8B.8B2AB2A8B2AB2A8B.8B$4.10B.9BA12BA9B.10B$3.12B.30B.
12B$3.13B.2B2.20B2.2B.13B$3.14B4.20B4.14B$2.15B4.8B.2B.8B4.15B$2.14B
6.6B6.6B6.14B$2.8BA5B7.B6.2A6.B7.5BA8B$3.6BA2BA6B7.A2.A.A2.A8.6BA2BA
6B$3.5BA4BA6B3.A2.4A2.3A7.6BA4BA5B$3.5BA3B2A7B2.3A4.2A3.2A.2A.7B2A3BA
5B$2.6BA5BA5B6.3A4.A2.A.A3.5BA5BA6B$9BA3BA6B3.3A2.7A.A.A3.6BA3BA9B$
13BA6B3.A2.A8.A.A.2A.6BA13B$20B.2A2.A.8A2.A.A2.20B$19B3.A.2A.A6.A.2A.
A3.19B$.17B4.A2.A.A.4A.A.A2.2A3.17B$.18B.2A.A.A.A.A2.A.A.A.A2.A.18B$.
18B.A2.A.A.A.A2.A.A.A.A.2A.18B$.17B3.2A2.A.A.4A.A.A2.A4.17B$19B3.A.2A
.A6.A.2A.A3.19B$20B2.A.A2.8A.A2.2A.20B$13BA6B.2A.A.A8.A2.A3.6BA13B$9B
A3BA6B3.A.A.7A2.3A3.6BA3BA9B$2.6BA5BA5B3.A.A2.A4.3A6.5BA5BA6B$3.5BA3B
2A7B.2A.2A3.2A4.3A2.7B2A3BA5B$3.5BA4BA6B7.3A2.4A2.A3.6BA4BA5B$3.6BA2B
A6B8.A2.A.A2.A7.6BA2BA6B$2.8BA5B7.B6.2A6.B7.5BA8B$2.14B6.6B6.6B6.14B$
2.15B4.8B.2B.8B4.15B$3.14B4.20B4.14B$3.13B.2B2.20B2.2B.13B$3.12B.30B.
12B$4.10B.9BA12BA9B.10B$5.8B.8B2AB2A8B2AB2A8B.8B$7.5B.8BABA14BABA8B.
5B$8.B3.38B3.B$12.8BA20BA8B$12.9BA3BA10BA3BA9B$11.11B3A12B3A11B$12.
38B$13.36B$13.36B$14.34B$15.32B$18.3B3.14B3.3B$25.12B$25.4B4.4B!

[confocaloid]

A non-symmetric 181-bitter fits, found by running LLS for several hours, may still be suboptimal:

Code: Select all

x = 70, y = 70, rule = B3/S23
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
obob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obobo
$2o66b2o2$2o66b2o$2o66b2o2$2o66b2o$2o66b2o2$2o66b2o$2o66b2o$27bo14bo$
2o23b2ob2o10b2ob2o23b2o$2o23b2ob2o10b2ob2o23b2o$25b2o2b2o8b2o2b2o$2o
24b2ob2o8b2ob2o24b2o$2o25bobo10bobo25b2o$28bo12bo$2o66b2o$2o66b2o2$2o
66b2o$2o66b2o$34b2o$2o11b3o14bo2bobo3bo14b3o11b2o$2o11b4o13b4obob3o2bo
10b4o11b2o$12bo3b2o10b2o5b2o3b3o9b2o3bo$2o11b2o3bo8bo2b5o3b2o11bo3b2o
11b2o$2o11b5o8bobobo4b3obob2o9b5o11b2o$15b2o9bobobob3o2bobobobo9b2o$2o
23b2obobobo2bobobobobo24b2o$2o24bobobobobobobob2ob2o23b2o$26bobobobobo
bobo4bo$2o22b2obobob2obobob5o2bo22b2o$2o22bo2bobo4bobo6b3o22b2o$25b2ob
ob3obob7o$2o24bobobo2bobo7bo24b2o$2o24bobo2bobo2b7obo23b2o$15b2o8b2ob
4o2bobo6bo9b2o$2o11b5o9bo4b3obob5o9b5o11b2o$2o11b2o3bo8bob3o3bob2o12bo
3b2o11b2o$12bo3b2o8b2obo2b2obo4b3o9b2o3bo$2o11b4o13bobobob4o2bo10b4o
11b2o$2o11b3o15bo2bobo2bo14b3o11b2o$34b2o$2o66b2o$2o66b2o2$2o66b2o$2o
66b2o$28bo12bo$2o25bobo10bobo25b2o$2o24b2ob2o8b2ob2o24b2o$25b2o2b2o8b
2o2b2o$2o23b2ob2o10b2ob2o23b2o$2o23b2ob2o10b2ob2o23b2o$27bo14bo$2o66b
2o$2o66b2o2$2o66b2o$2o66b2o2$2o66b2o$2o66b2o2$2o66b2o$obob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obobo$b2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o!
#C [[ GRID THEME Catagolue ]]

[Citation needed]

Since the "basic questions" thread is gone, would you make this thread sticky and add a link to the "basic questions" thread?

[hotdogPi]

Since the "basic questions" thread is gone, would you make this thread sticky and add a link to the "basic questions" thread?

It's still there.

viewtopic.php?f=17&t=2036

[hotcrystal0]

What's the smallest oscillator that contains every possible 3x3 configuration in CGoL?

[confocaloid]

What's the smallest oscillator that contains every possible 3x3 configuration in CGoL?

Similar questions are asked from time to time. To make it well-defined, you'll at least need to explain

• What is the metric. What exactly is meant by "smallest" (minimum single-phase bounding box area? envelope bounding box area? minimum population? maximum population? average population? envelope MCPS? minimum single-phase MCPS? sum of populations of all phases? rotor size? ...) Also in general, there may be more than one smallest example, so one could say for example either "what are oscillators with lowest minimum population..." or "what is the lowest minimum population of an oscillator...".
• What are the equivalence classes of configurations. Do you distinguish between all 2^9 = 512 3-by-3 configurations, or only between the 102 equivalence classes up to rotations and reflections (i.e. the possible "isotropic" conditions of a cell), or just between the 18 equivalence classes up to permutations of neighbours (i.e. the possible "outer-totalistic" conditions of a cell)? The latter would make sense since Conway's Life is outer-totalistic and someone might want to avoid introducing distinctions that are not already present in the rules.
• Are there any additional restrictions on the oscillators? (May or may not be interesting, depending on answers to the above questions.)

Explaining that doesn't guarantee that an exact answer can be found in practice, but at least would make the problem well-defined. In other words, there are actually many different questions hidden here.

[LuveelVoom]

Similar to the above question, how small a still life (in population) can be found that contains all (counting reflections and rotations) still life compatible 3x3 or 4x4 binary grids? We run into the problem at 4x4 of even enumerating these grids, due to the coolout conjecture. How does one tell whether a given grid is a violation of the CC?

[confocaloid]

[...]

A 180-cell solution found using the symmetry constraint "-s C4" with the above LLS input file. Still no proof of optimality. [...]

[...] A non-symmetric 181-bitter fits, found by running LLS for several hours, may still be suboptimal: [...]

So far neither a (182+)-bit solution nor "unsatisfiable", after running LLS/kissat for ~3 weeks of clock time with the same input. So the problem remains open, and might be hard. (And then there might be other solutions where the still life nontrivially interacts with Karel's p177, or at least touches the rotor.)

EDIT 2025-02-04: interrupted the search before completion, without either finding a solution or getting "unsatisfiable". The question remains open.
EDIT 2025-01-24: still running, still no result (either positive or negative).

Code: Select all

299
Getting search pattern...
Done

Preprocessing...
Done

Width: 34
Height: 34
Duration: 2

Number of undetermined cells: 368
Number of variables: 3527
Number of clauses: 112694

x = 34, y = 34, rule = B3/S23
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbboobbbbbbbbbboobbbbbbbbbb$
bbbbbbbbbbbobbbbbbbbbbobbbbbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbboboooobboobboooobobbbbbbbb$
bbbbbbbbobobbobbbbbbobbobobbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbbbbbbbobbobobbobbbbbbbbbbbb$
bbbboobbbbbboboboboooobbobbboobbbb$
bbbobboboobobbobobbbbbooobbobbobbb$
bobboobbbobooooboooooobbbbbboobbob$
boobobbbbobbbbbobbbbbboobobbboboob$
bbbbobbooboooobboooooboboobbbobbbb$
bbbboobbobobbooobbbbobobbbbboobbbb$
bbbbbbbbobobbbbboooboboooobbbbbbbb$
bbbbbbbooboooooobbobobbbbbobbbbbbb$
bbboobobbbbbbbbbbobbooooobboboobbb$
bbbooboooooooboooobobbbbooooboobbb$
bbbbbbbbbbbbobobbbboooobbbbbbbbbbb$
bbbbbbbbooobobboboobbboooobbbbbbbb$
bbbboobobboboboobobbobbbbboboobbbb$
bbbbobbbobobobbobobooooobobbbobbbb$
boobobbbboobobbobobbbbboobbbboboob$
bobboobbbbbboooobboooobbbbbboobbob$
bbbobbobbooobbbboobbbbooobbobbobbb$
bbbboobbbobboooobboooobbobbboobbbb$
bbbbbbbbbbbbobbobbobbobbbbbbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbbobobbobbbbbbobbobobbbbbbbb$
bbbbbbbboboooobboobboooobobbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbbbbbobbbbbbbbbbobbbbbbbbbbb$
bbbbbbbbbboobbbbbbbbbboobbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb!


Total solver time: 3667.33225440979
300
Getting search pattern...
Done

Preprocessing...
Done

Width: 34
Height: 34
Duration: 2

Number of undetermined cells: 368
Number of variables: 3529
Number of clauses: 112718

x = 34, y = 34, rule = B3/S23
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbboobbbbbbbbbboobbbbbbbbbb$
bbbbbbbbbbbobbbbbbbbbbobbbbbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbboboooobboobboooobobbbbbbbb$
bbbbbbbbobobbobbbbbbobbobobbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbbbbbbobbobobbobbbbbbbbbbbbb$
bbbboobbbbbboooobbooooobbbbboobbbb$
bbbobbobbboobbbboobbbbbobbbobbobbb$
bobboobbboboboobbbooooobobbboobbob$
boobobbbbobobboooobbbbbbobbbboboob$
bbbbobboobobobbbboboooooboobbobbbb$
bbbboobboboboooobobobbbobobboobbbb$
bbbbbbbbobobbbbobobboobobobbbbbbbb$
bbbbbbboobooooobbooobbooboobbbbbbb$
bbboobobbobbbbobobbbobbbobboboobbb$
bbboobooboboobobooooboobobooboobbb$
bbbbbbbboboboboobbbobobobobbbbbbbb$
bbbbbbbbobobobbbboobbobobobbbbbbbb$
bbbboobooboboooooboboobobooboobbbb$
bbbbobbbobobbbbbobobbobobobbbobbbb$
boobobbboboooobbobobobbobobbboboob$
bobboobbbobbbooobbobooobobbboobbob$
bbbobbobbboobbbboobbbbbobbbobbobbb$
bbbboobbbbbboooobbooooobbbbboobbbb$
bbbbbbbbbbbbobbobobbobbbbbbbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbbobobbobbbbbbobbobobbbbbbbb$
bbbbbbbboboooobboobboooobobbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbbbbbobbbbbbbbbbobbbbbbbbbbb$
bbbbbbbbbboobbbbbbbbbboobbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb!


Total solver time: 3101.3477153778076
301
Getting search pattern...
Done

Preprocessing...
Done

Width: 34
Height: 34
Duration: 2

Number of undetermined cells: 368
Number of variables: 3531
Number of clauses: 112738

x = 34, y = 34, rule = B3/S23
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbboobbbbbbbbbboobbbbbbbbbb$
bbbbbbbbbbbobbbbbbbbbbobbbbbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbboboooobboobboooobobbbbbbbb$
bbbbbbbbobobbobbbbbbobbobobbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbbbbbbobbobobbbobbbbbbbbbbbb$
bbbboobbbbbboooobobooobbobbboobbbb$
bbbobbobbboobbbbboobbbooobbobbobbb$
bobboobbbobbooooobbboobbbbbboobbob$
boobobbbobobobbbboooboboobbbboboob$
bbbbobbbobobobooobbobobobobbbobbbb$
bbbbooboobobobobbobobobobobboobbbb$
bbbbbbbbobobobobobobobooboobbbbbbb$
bbbbbbbbobobobobobobobbbbobbbbbbbb$
bbboobooboboboobobobooooobboboobbb$
bbboobobbobobbbbobobbbbbboooboobbb$
bbbbbbboobobooobobooooooobbbbbbbbb$
bbbbbbbbobobobbobobbbbbbbobbbbbbbb$
bbbboobbobobbobobboooooooboboobbbb$
bbbbobbooboooobbobobbbbbbobbbobbbb$
boobobbbbobbbbooobobooooobbbboboob$
bobboobbbobooobbboboobbbbbbboobbob$
bbbobboboobobboobobbbbooobbobbobbb$
bbbboobbbbbboboboboooobbobbboobbbb$
bbbbbbbbbbbbbobbobobbobbbbbbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbbobobbobbbbbbobbobobbbbbbbb$
bbbbbbbboboooobboobboooobobbbbbbbb$
bbbbbbbbbobbbbbboobbbbbbobbbbbbbbb$
bbbbbbbbbbbobbbbbbbbbbobbbbbbbbbbb$
bbbbbbbbbboobbbbbbbbbboobbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb!


Total solver time: 37058.69650745392
302
Getting search pattern...
Done

Preprocessing...
Done

Width: 34
Height: 34
Duration: 2

Number of undetermined cells: 368
Number of variables: 3533
Number of clauses: 112754

[hotcrystal0]

What programming language can simulate CGoL with the least amount of commands?

[confocaloid]

What programming language can simulate CGoL with the least amount of commands?

Related (Code Golf and Coding Challenges Stack Exchange):
https://codegolf.stackexchange.com/ques ... me-of-life Shortest Game of Life
https://codegolf.stackexchange.com/ques ... r-automata Questions tagged [cellular-automata]
https://codegolf.stackexchange.com/ques ... me-of-life Questions tagged [game-of-life]

Related (Stack Overflow, "locked because the question is off-topic but has historical significance")
https://stackoverflow.com/questions/349 ... me-of-life Code Golf: Conway's Game of Life

[get_Snacked]

i'm pretty sure it can be proven pretty easily that the maximum amount of cells from one generation to the next in B3/S23 is 3p, where p is the population at the before-generation.
here are some agars that showcase this maximum:

Code: Select all

x = 7, y = 9, rule = B3/S23:T9,9
o2bo2bo$o2bo2bo$o2bo2bo$o2bo2bo$o2bo2bo$o2bo2bo$o2bo2bo$o2bo2bo$o2bo2b
o!
[[ SHOWGENSTATS ]]

Code: Select all

x = 9, y = 9, rule = B3/S23:T9,9
bo2bo2bo$2bo2bo2bo$o2bo2bo$bo2bo2bo$2bo2bo2bo$o2bo2bo$bo2bo2bo$2bo2bo
2bo$o2bo2bo!
[[ SHOWGENSTATS ]]

ćode+x = 9, y = 9, rule = B3/S23:T9,9
bo2bo2bo$o2bo2bo$o2bo2bo$2bo2bo2bo$2bo2bo2bo$bo2bo2bo$bo2bo2bo$o2bo2b
o$o2bo2bo!
code+
now, what about extending this question to ask what the maximum amount of cells from one generation to two generations after is in B3-S23_ what about three generations, four generation, and so on_

[MathAndCode]

What can be said about the function f(n) for higher n? In particular, is f(n) = 0 for some n > 2?

I suspect that there is a certain value of n past which f(n) is never zero. Consider this trecentuply-long barge polynomino pedecessor (based on a crab-based tubstretcher):

Code: Select all

x = 659, y = 654, rule = B3/S23
2bo$3o$2bo$b2o$bo$2o2bo$8o$2b2o3bo$7bo$7bo$7b5o$11bo$11bo$11bo$11b5o$
15bo$15bo$15bo$15b5o$19bo$19bo$19bo$19b5o$23bo$23bo$23bo$23b5o$27bo$27b
o$27bo$27b5o$31bo$31bo$31bo$31b5o$35bo$35bo$35bo$35b5o$39bo$39bo$39bo
$39b5o$43bo$43bo$43bo$43b5o$47bo$47bo$47bo$47b5o$51bo$51bo$51bo$51b5o
$55bo$55bo$55bo$55b5o$59bo$59bo$59bo$59b5o$63bo$63bo$63bo$63b5o$67bo$
67bo$67bo$67b5o$71bo$71bo$71bo$71b5o$75bo$75bo$75bo$75b5o$79bo$79bo$79b
o$79b5o$83bo$83bo$83bo$83b5o$87bo$87bo$87bo$87b5o$91bo$91bo$91bo$91b5o
$95bo$95bo$95bo$95b5o$99bo$99bo$99bo$99b5o$103bo$103bo$103bo$103b5o$107b
o$107bo$107bo$107b5o$111bo$111bo$111bo$111b5o$115bo$115bo$115bo$115b5o
$119bo$119bo$119bo$119b5o$123bo$123bo$123bo$123b5o$127bo$127bo$127bo$
127b5o$131bo$131bo$131bo$131b5o$135bo$135bo$135bo$135b5o$139bo$139bo$
139bo$139b5o$143bo$143bo$143bo$143b5o$147bo$147bo$147bo$147b5o$151bo$
151bo$151bo$151b5o$155bo$155bo$155bo$155b5o$159bo$159bo$159bo$159b5o$
163bo$163bo$163bo$163b5o$167bo$167bo$167bo$167b5o$171bo$171bo$171bo$171b
5o$175bo$175bo$175bo$175b5o$179bo$179bo$179bo$179b5o$183bo$183bo$183b
o$183b5o$187bo$187bo$187bo$187b5o$191bo$191bo$191bo$191b5o$195bo$195b
o$195bo$195b5o$199bo$199bo$199bo$199b5o$203bo$203bo$203bo$203b5o$207b
o$207bo$207bo$207b5o$211bo$211bo$211bo$211b5o$215bo$215bo$215bo$215b5o
$219bo$219bo$219bo$219b5o$223bo$223bo$223bo$223b5o$227bo$227bo$227bo$
227b5o$231bo$231bo$231bo$231b5o$235bo$235bo$235bo$235b5o$239bo$239bo$
239bo$239b5o$243bo$243bo$243bo$243b5o$247bo$247bo$247bo$247b5o$251bo$
251bo$251bo$251b5o$255bo$255bo$255bo$255b5o$259bo$259bo$259bo$259b5o$
263bo$263bo$263bo$263b5o$267bo$267bo$267bo$267b5o$271bo$271bo$271bo$271b
5o$275bo$275bo$275bo$275b5o$279bo$279bo$279bo$279b5o$283bo$283bo$283b
o$283b5o$287bo$287bo$287bo$287b5o$291bo$291bo$291bo$291b5o$295bo$295b
o$295bo$295b5o$299bo$299bo$299bo$299b5o$303bo$303bo$303bo$303b5o$307b
o$307bo$307bo$307b5o$311bo$311bo$311bo$311b5o$315bo$315bo$315bo$315b5o
$319bo$319bo$319bo$319b5o$323bo$323bo$323bo$323b5o$327bo$327bo$327bo$
327b5o$331bo$331bo$331bo$331b5o$335bo$335bo$335bo$335b5o$339bo$339bo$
339bo$339b5o$343bo$343bo$343bo$343b5o$347bo$347bo$347bo$347b5o$351bo$
351bo$351bo$351b5o$355bo$355bo$355bo$355b5o$359bo$359bo$359bo$359b5o$
363bo$363bo$363bo$363b5o$367bo$367bo$367bo$367b5o$371bo$371bo$371bo$371b
5o$375bo$375bo$375bo$375b5o$379bo$379bo$379bo$379b5o$383bo$383bo$383b
o$383b5o$387bo$387bo$387bo$387b5o$391bo$391bo$391bo$391b5o$395bo$395b
o$395bo$395b5o$399bo$399bo$399bo$399b5o$403bo$403bo$403bo$403b5o$407b
o$407bo$407bo$407b5o$411bo$411bo$411bo$411b5o$415bo$415bo$415bo$415b5o
$419bo$419bo$419bo$419b5o$423bo$423bo$423bo$423b5o$427bo$427bo$427bo$
427b5o$431bo$431bo$431bo$431b5o$435bo$435bo$435bo$435b5o$439bo$439bo$
439bo$439b5o$443bo$443bo$443bo$443b5o$447bo$447bo$447bo$447b5o$451bo$
451bo$451bo$451b5o$455bo$455bo$455bo$455b5o$459bo$459bo$459bo$459b5o$
463bo$463bo$463bo$463b5o$467bo$467bo$467bo$467b5o$471bo$471bo$471bo$471b
5o$475bo$475bo$475bo$475b5o$479bo$479bo$479bo$479b5o$483bo$483bo$483b
o$483b5o$487bo$487bo$487bo$487b5o$491bo$491bo$491bo$491b5o$495bo$495b
o$495bo$495b5o$499bo$499bo$499bo$499b5o$503bo$503bo$503bo$503b5o$507b
o$507bo$507bo$507b5o$511bo$511bo$511bo$511b5o$515bo$515bo$515bo$515b5o
$519bo$519bo$519bo$519b5o$523bo$523bo$523bo$523b5o$527bo$527bo$527bo$
527b5o$531bo$531bo$531bo$531b5o$535bo$535bo$535bo$535b5o$539bo$539bo$
539bo$539b5o$543bo$543bo$543bo$543b5o$547bo$547bo$547bo$547b5o$551bo$
551bo$551bo$551b5o$555bo$555bo$555bo$555b5o$559bo$559bo$559bo$559b5o$
563bo$563bo$563bo$563b5o$567bo$567bo$567bo$567b5o$571bo$571bo$571bo$571b
5o$575bo$575bo$575bo$575b5o$579bo$579bo$579bo$579b5o$583bo28bo$583bo26b
5o16bobo2b2o$583bo23b4o2b2o16b7o$583b5o19b2o4bo22b5o$587bo18b2o4b2o22b
o2bo$587bo18b2o4bo22b2o2b2o$587bo18b2o3b2o20b3o4bo$587b5o13b2o4bo22bo
5b2o$591bo13b2o4bo22b2o5bo$591bo14b2o26b2o5bo$591bo15b3ob3o21b2o$591b
6ob4o5b7o21b5o2bo$596b8o2b2obo27b3o2b4o$596bo3bo2bo2b2obobo26bo6b2o$596b
ob2o3b2obo2b3o26bo7bo$596bob2o4b3o31bobo2bo2bo$596b4o4b5o28b11o$597b3o
5b6o7b5o12b3o3bo3b2o$597bo5bo3b6ob5o3b5o7b2o$597b5obo7b4o11bo3b5o$599b
5o10bo9bob5o$600b2o12b2o4bo3b5o$600bo14b3o2b4o3b3o$600bo14b7obo4bo$600b
o18bo7b2o$599b2o17b2o7bo$599bo17b3o6b2o$599bo17b3o4bob3o$599b2o17bo4b
2ob2o$600bo17bo5bob2o$600bo17b2o4b4o$600bo17b2o4bo2b2o$600bo18bo4bo3b
o$600b2o17bo8bo$599b3o21b2o3bo2b2obo2b4o$599b2o21b3o2b11obo$600bo19bo
3b4o4bob2o3bo$600b2o18bo2b2o10bo$601bo17b5o11b2o$599b3o17b2o2bo11b2o3b
5o$601bo34bo3bobo4bo$636b3obo6b3o$637b8ob2obo$639b2ob5o2b2o$637b3o3bo
5b2o$647bobo$647b3o$638b3o7b3o$631b14obobo$614b5o2bo5b5o5b4obobob3o$610b
2o4bob10o11bo4b3o$611b2o7b2o17bo4b3o$611bo8bo17b2o6b2o2b4o$611b2o3bo2b
2o17bo7b5obo$610b10o17b4o5b3o3bo$612bobo22b2ob3o4bo$641b3o3bo$642b2o3b
2o$642bo5b2o$641b2o5b2o$641bo6b3o$641b3o6b3ob5o$641bo9b4obo$651b2o$652b
4o$654b4o$654bo2bo$653b2o$653bo$653b3o$653bo!

While it is probably inefficient, I am sure that there is a point past which the minimum polynomino predecessor size for an n-tuply long barge increases by four bits per two bits, where the unsimplified rate is four bits per two bits and not sixteen bits per eight bits because different zig-zag sizes can be used and connected together, as demonstrated below.

Code: Select all

x = 659, y = 654, rule = B3/S23
2bo$3o$2bo$b2o$bo$2o2bo$8o$2b2o3bo$7bo$7bo$7b5o$11bo$11bo$11bo$11b5o$
15bo$15bo$15bo$15b5o$19bo$19bo$19bo$19b5o$23bo$23bo$23bo$23b5o$27bo$27b
o$27bo$27b5o$31bo$31bo$31bo$31b5o$35bo$35bo$35bo$35b5o$39bo$39bo$39bo
$39b5o$43bo$43bo$43bo$43b5o$47bo$47bo$47bo$47b5o$51bo$51bo$51bo$51b5o
$55bo$55bo$55bo$55b5o$59bo$59bo$59bo$59b5o$63bo$63bo$63b4o$66bo$66bo$
66b4o$69bo$69bo$69b4o$72bo$72bo$72b4o$75bo$75bo$75b4o$78bo$78bo$78b4o
$81bo$81bo$81b4o$84bo$84bo$84b4o$87bo$87bo$87b4o$90bo$90bo$90b4o$93bo
$93bo$93b4o$96bo$96bo$96b4o$99bo$99bo$99b4o$102bo$102bo$102b4o$105bo$
105bo$105b4o$108bo$108bo$108b4o$111bo$111bo$111b4o$114bo$114bo$114b4o
$117bo$117bo$117b4o$120bo$120bo$120b4o$123bo$123bo$123b4o$126bo$126bo
$126b4o$129bo$129bo$129b4o$132bo$132bo$132b4o$135bo$135bo$135b4o$138b
o$138bo$138b4o$141bo$141bo$141b4o$144bo$144bo$144b4o$147bo$147bo$147b
4o$150bo$150bo$150b4o$153bo$153bo$153b4o$156bo$156bo$156b4o$159bo$159b
o$159b4o$162bo$162bo$162b4o$165bo$165bo$165b4o$168bo$168bo$168b4o$171b
o$171bo$171b4o$174bo$174bo$174b4o$177bo$177bo$177b4o$180bo$180bo$180b
4o$183bo$183bo$183b4o$186bo$186bo$186b4o$189bo$189bo$189b4o$192bo$192b
o$192b4o$195bo$195bo$195b4o$198bo$198bo$198b4o$201bo$201bo$201b4o$204b
o$204bo$204b4o$207bo$207bo$207b4o$210bo$210bo$210b4o$213bo$213bo$213b
4o$216bo$216bo$216b4o$219bo$219bo$219bo$219b5o$223bo$223bo$223bo$223b
5o$227bo$227bo$227bo$227b5o$231bo$231bo$231bo$231b5o$235bo$235bo$235b
o$235b5o$239bo$239bo$239bo$239b5o$243bo$243bo$243bo$243b5o$247bo$247b
o$247bo$247b5o$251bo$251bo$251bo$251b5o$255bo$255bo$255bo$255b5o$259b
o$259bo$259bo$259b5o$263bo$263bo$263bo$263b5o$267bo$267bo$267bo$267b5o
$271bo$271bo$271bo$271b5o$275bo$275bo$275bo$275b5o$279bo$279bo$279bo$
279b5o$283bo$283bo$283bo$283b5o$287bo$287bo$287bo$287b5o$291bo$291bo$
291bo$291b5o$295bo$295bo$295bo$295b5o$299bo$299bo$299bo$299b6o$304bo$
304bo$304bo$304bo$304b6o$309bo$309bo$309bo$309bo$309b6o$314bo$314bo$314b
o$314bo$314b6o$319bo$319bo$319bo$319bo$319b6o$324bo$324bo$324bo$324bo
$324b6o$329bo$329bo$329bo$329bo$329b6o$334bo$334bo$334bo$334bo$334b6o
$339bo$339bo$339bo$339bo$339b6o$344bo$344bo$344bo$344bo$344b6o$349bo$
349bo$349bo$349bo$349b6o$354bo$354bo$354bo$354bo$354b6o$359bo$359bo$359b
o$359bo$359b6o$364bo$364bo$364bo$364bo$364b6o$369bo$369bo$369bo$369bo
$369b6o$374bo$374bo$374bo$374bo$374b6o$379bo$379bo$379bo$379bo$379b6o
$384bo$384bo$384bo$384bo$384b6o$389bo$389bo$389bo$389bo$389b6o$394bo$
394bo$394bo$394bo$394b6o$399bo$399bo$399bo$399bo$399b6o$404bo$404bo$404b
o$404bo$404b6o$409bo$409bo$409bo$409bo$409b6o$414bo$414bo$414bo$414bo
$414b6o$419bo$419bo$419bo$419bo$419b6o$424bo$424bo$424bo$424bo$424b6o
$429bo$429bo$429bo$429bo$429b6o$434bo$434bo$434bo$434bo$434b6o$439bo$
439bo$439bo$439bo$439b6o$444bo$444bo$444bo$444bo$444b6o$449bo$449bo$449b
o$449bo$449b6o$454bo$454bo$454bo$454bo$454b6o$459bo$459bo$459bo$459bo
$459b6o$464bo$464bo$464bo$464bo$464b6o$469bo$469bo$469bo$469bo$469b6o
$474bo$474bo$474bo$474bo$474b6o$479bo$479bo$479bo$479bo$479b6o$484bo$
484bo$484bo$484bo$484b6o$489bo$489bo$489bo$489bo$489b6o$494bo$494bo$494b
o$494bo$494b6o$499bo$499bo$499bo$499bo$499b5o$503bo$503bo$503bo$503b5o
$507bo$507bo$507bo$507b5o$511bo$511bo$511bo$511b5o$515bo$515bo$515bo$
515b5o$519bo$519bo$519bo$519b5o$523bo$523bo$523bo$523b5o$527bo$527bo$
527bo$527b5o$531bo$531bo$531bo$531b5o$535bo$535bo$535bo$535b5o$539bo$
539bo$539bo$539b5o$543bo$543bo$543bo$543b5o$547bo$547bo$547bo$547b5o$
551bo$551bo$551bo$551b5o$555bo$555bo$555bo$555b5o$559bo$559bo$559bo$559b
5o$563bo$563bo$563bo$563b5o$567bo$567bo$567bo$567b5o$571bo$571bo$571b
o$571b5o$575bo$575bo$575bo$575b5o$579bo$579bo$579bo$579b5o$583bo28bo$
583bo26b5o16bobo2b2o$583bo23b4o2b2o16b7o$583b5o19b2o4bo22b5o$587bo18b
2o4b2o22bo2bo$587bo18b2o4bo22b2o2b2o$587bo18b2o3b2o20b3o4bo$587b5o13b
2o4bo22bo5b2o$591bo13b2o4bo22b2o5bo$591bo14b2o26b2o5bo$591bo15b3ob3o21b
2o$591b6ob4o5b7o21b5o2bo$596b8o2b2obo27b3o2b4o$596bo3bo2bo2b2obobo26b
o6b2o$596bob2o3b2obo2b3o26bo7bo$596bob2o4b3o31bobo2bo2bo$596b4o4b5o28b
11o$597b3o5b6o7b5o12b3o3bo3b2o$597bo5bo3b6ob5o3b5o7b2o$597b5obo7b4o11b
o3b5o$599b5o10bo9bob5o$600b2o12b2o4bo3b5o$600bo14b3o2b4o3b3o$600bo14b
7obo4bo$600bo18bo7b2o$599b2o17b2o7bo$599bo17b3o6b2o$599bo17b3o4bob3o$
599b2o17bo4b2ob2o$600bo17bo5bob2o$600bo17b2o4b4o$600bo17b2o4bo2b2o$600b
o18bo4bo3bo$600b2o17bo8bo$599b3o21b2o3bo2b2obo2b4o$599b2o21b3o2b11obo
$600bo19bo3b4o4bob2o3bo$600b2o18bo2b2o10bo$601bo17b5o11b2o$599b3o17b2o
2bo11b2o3b5o$601bo34bo3bobo4bo$636b3obo6b3o$637b8ob2obo$639b2ob5o2b2o
$637b3o3bo5b2o$647bobo$647b3o$638b3o7b3o$631b14obobo$614b5o2bo5b5o5b4o
bobob3o$610b2o4bob10o11bo4b3o$611b2o7b2o17bo4b3o$611bo8bo17b2o6b2o2b4o
$611b2o3bo2b2o17bo7b5obo$610b10o17b4o5b3o3bo$612bobo22b2ob3o4bo$641b3o
3bo$642b2o3b2o$642bo5b2o$641b2o5b2o$641bo6b3o$641b3o6b3ob5o$641bo9b4o
bo$651b2o$652b4o$654b4o$654bo2bo$653b2o$653bo$653b3o$653bo!

This takes care of one modular residue class modulo four, and I suspect that there are others ways to cap one of the ends (e.g., n-tuply long boat, n-tuply long boat tie boat, and n-tuply long boat tie ship) that cover the other three modular residue classes. If this indeed works, then all sufficiently large integers n have f(n)≠0.



By the way, generation one of your dodecomino great-great-great-great-great-great-great-great-grandparent of mirrored tables has a ten-cell child that I did not previously have in my repository of minimally-sized predecessors, and I found some ten-cell parents (which I didn't have either). I shall add these to my repository, but did your search results any other minimally-sized predecessors of any object that I might be interested in? I know that we are not searching for exactly the same thing, but searches for either could potentially yield useful results for searches for the other.

Code: Select all

x = 397, y = 7, rule = B3/S23
3bo13bo13bo16bo13bo13bo16bo13bo13bo16bo13bo13bo16bo13bo13bo16bo13bo13b
o16bo13bo13bo16bo13bo13bo16bo13bo13bo$227bo14bo14bo14bo14bo14bo14bo14b
o14bo14bo14bo14bo$3o3bo9b2o3bo9b2o3bo8b3o2bo10b2o2bo10b2o2bo9b3o2b2o9b
2o2b2o9b2o2b2o8b3o2bo10b2o2bo10b2o2bo9b3o2b2o9b2o2b2o9b2o2b2o8b2o3bo10b
o3bo10bo3bo9b2o3b2o9bo3b2o9bo3b2o8b2o3bo10bo3bo10bo3bo9b2o3b2o9bo3b2o
9bo3b2o$4b2o9bo3b2o9bo3b2o13bobo8bo3bobo8bo3bobo12bo10bo3bo10bo3bo14b
obo8bo3bobo8bo3bobo12bo10bo3bo10bo3bo14bobo8bo3bobo8bo3bobo12bo10bo3b
o10bo3bo14bobo8bo3bobo8bo3bobo12bo10bo3bo10bo3bo$3bo14bo14bo14bo14bo14b
o14bo14bo14bo14bo14bo14bo14bo14bo14bo13b2o13b2o13b2o13b2o13b2o13b2o13b
2o13b2o13b2o13b2o13b2o13b2o$3bo14bo14bo13bo14bo14bo14bo14bo14bo14bo14b
o14bo14bo14bo14bo$2bo14bo14bo14bo14bo14bo14bo14bo14bo15bo14bo14bo14bo
14bo14bo13bo14bo14bo14bo14bo14bo15bo14bo14bo14bo14bo14bo!

[confocaloid]

[...] did your search results any other minimally-sized predecessors of any object that I might be interested in? [...]

If I remember correctly, then all output of that search is already posted in the stamp collection in the earlier post. I only searched up to 12 bits (using a naive slow approach that computes the set of n-ominoes by adding one bit to every (n-1)-omino in every possible way and removing duplicates), and the only output was a collection of polyominoes evolving into strict objects, filtered to leave only smallest polyomino predecessor(s) for every resulting object. It shouldn't be too hard to go beyond 12 bits with faster algorithms, and to collect more 'interesting' information than my script collected.

[hotcrystal0]

What's the smallest oscillator that contains every possible 3x3 configuration in CGoL?

I think I need to reword this. What is the smallest oscillator, that in one phase, contains every possible 3x3 configuration not counting rotation and reflection?

[WhiteHawk]

What is the smallest asymmetric true-period glider gun with more than 1 barrel in life?

If that answer is the p60 glider gun, then what is the second smallest in that category without period-multiplying streams?

EDIT: Another advanced question: Is there a true-period oscillator for every period p that has cells on for every n/p, where n is an integer less than or equal to P. (Based on the new LV feature for tracking how long cells are on in an oscillator)? If so, what is the smallest oscillator for each period with this property, up to some limit?

Oscillators for periods 2-16: Blinker, Caterer, Mold, Fumarole, P6 Shuttle, 28p7.3, Coe's P8, 48p9, P10 TL hassler, Diamondback, 127p12, 104p13, 94p14, Eater on PD in 102P15, and 90p16 (TL/R Hassler). I couldn't find a non-weld solution for P17.

[Sylvani]

Is there a well-defined method for making constructed ships like the Waterbear or the Caterpillar? I have a few reactions in some non-CGOL cellular automata that I want to make something similar with. How do people engineer stuff like this?

[WhiteHawk]

Is there a well-defined method for making constructed ships like the Waterbear or the Caterpillar? I have a few reactions in some non-CGOL cellular automata that I want to make something similar with. How do people engineer stuff like this?

Shorthand: No.

Longhand: It depends on the versatility of the reaction in question, the need for cleanup, the need for wick construction, and the slope. As for how this works, there are several threads on the forums where problems were tackled to build such ships.

[dvgrn]

Longhand: It depends on the versatility of the reaction in question, the need for cleanup, the need for wick construction, and the slope. As for how this works, there are several threads on the forums where problems were tackled to build such ships.

Slightly longer:

Some moving reactions are close enough to spaceships that multiple copies can support each other directly, like switch engines in Corderships.

Some reactions can be made to be self-supporting using some kind of reburnable fuse. The easier projects are the ones using moving reactions that are slow enough that the fuse can be built ahead of the reaction by colliding gliders and/or forward-travelling xWSSes (like the shield bug/centipede/silverfish/water strider).

The trickier projects have active reactions that move too fast for gliders to keep up with, so they need a helix.

Depending on the non-CA rule (EDIT: sorry, non-CGoL rule) that you're talking about, you might have to substitute other small natural spaceships for the gliders or xWSSes in the linked examples.

[confocaloid]

^^ The part "non-CA rule" seems to be a misnomer. Cellular automata other than Conway's Life might be too numerous with too many possibilities to decide where to focus, but there are certainly some good choices (including those early investigated) and lots of unexplored territory. They aren't CGoL, but they definitely are CA.

I have a few reactions in some non-CGOL cellular automata that I want to make something similar with. How do people engineer stuff like this?

Links to some related discussions / forum threads:
viewtopic.php?p=177140#p177140 Re: Thread for your CA software/algorithms ideas
viewtopic.php?f=11&t=5933 Thread for your corderization requests
viewtopic.php?p=148749#p148749 Re: Thread for basic non-CGOL questions

[Sylvani]

^^ The part "non-CA rule" seems to be a misnomer.

Oops, my bad. I meant to say "non-CGOL rule", as in anything that isn't B3/S23

EDIT by dvgrn:: This note of mine isn't worth a separate post, but that's basically what you did say -- the typo was mine, not yours ...

[Vlev2]

i don't know if this is an advanced question
but how do i make multistate/colorized rules other than generations rules?

[dvgrn]

i don't know if this is an advanced question
but how do i make multistate/colorized rules other than generations rules?

The details can get pretty advanced, for sure.

There's a LifeWiki tutorial, which expands on the documentation in Golly. What kind of rule are you trying to create?

[b-engine]

i don't know if this is an advanced question
but how do i make multistate/colorized rules other than generations rules?

Ruletables are usually defined with this header:

Code: Select all

@RULE name
@TABLE 
n_states:3
neighborhood:Moore
symmetries:rotate4reflect

N_states could be any numbers between 2 and 256.
Neighborhood could be Moore, vonNeumann or Hexagonal (as far as I know).
Symmetries could be permute, rotate4reflect, rotate8reflect (only for Moore rules), rotate6reflect (only for hexagonal rules), as far as I know.

Variables are defined like this:

Code: Select all

var a = {0,1,2}

Separate variables with any names (without whitespace) could be defined:

Code: Select all

var a = {0,1,2}
var a1 = {0,1,2}
var b = {0,1,2}

Or defined to be the same as another variable:

Code: Select all

var a={0,1,2}
var a1=a
var a2=a
var a3=a
var a4=a
var a5=a
var a6=a
var a7=a
var a8=a

Transitions could be defined as this:

Code: Select all

0,1,1,1,0,0,0,0,0,1

Or this:

Code: Select all

0,a,b,c,0,0,0,0,0,2

Or this:

Code: Select all

0,a,a,a,0,0,0,0,0,2 # this means that all three cells must be the same state to satisfy the conditions.

If you want all cells to die unless specified, do this:

Code: Select all

var a={0,1,2}
var a1=a
var a2=a
var a3=a
var a4=a
var a5=a
var a6=a
var a7=a
var a8=a

# Put everything else here

a,a1,a2,a3,a4,a5,a6,a7,a8,0

Colors and names could also be defined:

Code: Select all

@COLORS
1 255 128 0 
2 0 128 255 
@NAMES 
1 First name
2 Second name

[confocaloid]

i don't know if this is an advanced question
but how do i make multistate/colorized rules other than generations rules?

Some notes/corrections/clarifications to what was posted above:

• To ensure compatibility, the .rule filename (and the name given after '@RULE ') must begin with an uppercase English letter, and must contain only English letters and/or digits. The hyphens and underscores are allowed if you need separators.
• Colors and names are optional, you can just omit them for simplicity.
• Repeating occurrences of a variable name in a single rule (in a single line) refer to the same variable. For example, if the variable "a" is defined as

  Code: Select all

  var a={0,1}

  then the following rule:

  Code: Select all

  3, a,a,a,a,a,a,a,a, 5

  will be equivalent to the following two rules:

  Code: Select all

  3, 0,0,0,0,0,0,0,0, 5
  3, 1,1,1,1,1,1,1,1, 5
  

  which can be compared with how variables are treated in mathematics. When the same name is used more than once in a single rule, it refers to the same variable. Different names refer to different variables.
• In general, be careful with local jargon. It often differs in various ways from the more widely used Life/CA-related terminology.
  
  To give one example, a line in the "@TABLE" section of a ruletable such as

  Code: Select all

  0,1,1,1,0,0,0,0,0,1

  is correctly described as a rule or a transition rule (multiple sources can be provided if requested). Such a line essentially defines one of "prescribed rules" that all patterns must follow.
  
  However, people here on the forums often use the jargon "transition" instead to refer to the same thing. This jargon is "locally frequent", but technically incorrect and does not appear to match either wider usage or common-sense intuition.

[confocaloid]

[...] What would it take to prove that Pentapole is the only possible 11-cell oscillator in B3/S23? [...]

Case-by-case-analysis? Determine all possible imaginable ways how an oscillator might have a phase with precisely 11 bits (alive cells), and for every such possibility prove that it doesn't happen in CGoL.

Related discussions:
viewtopic.php?p=154067#p154067
viewtopic.php?p=192115#p192115

Some of the imaginable possibilities are:

• A glider hitting a 6-bit object. This example isn't an oscillator, but some other arrangement might be an oscillator:

  Code: Select all

  x = 14, y = 4, rule = B3/S23
  obo9bo$b2o8b3o$bo11bo$13bo!
  

• A glider hitting two blinkers. This example isn't an oscillator, but some other arrangement might be an oscillator:

  Code: Select all

  x = 16, y = 29, rule = B3/S23
  3o18$7bo$5bobo$6b2o6$15bo$15bo$15bo!
  

• R-pentomino hitting a 6-bit object.
• R-pentomino hitting two blinkers.
• Some 6-bit object hitting a boat.
• Some 7-bit object hitting a block.
• Some 8-bit object hitting a blinker. This example isn't an oscillator, but some other arrangement might be an oscillator:

  Code: Select all

  x = 20, y = 13, rule = B3/S23
  16b2o$17bobo$17b3o$18bo9$3o!
  

• A single 11-bit object (either a polyomino, or a polyplet, or any other 11-bit cluster where all cells will interact in the next tick).