Canonical list of still lifes in script-readable form?

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pcallahan
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Canonical list of still lifes in script-readable form?

Post by pcallahan » June 24th, 2021, 11:34 am

Sorry if this is something I should be able to find. I know we have carefully curated enumerations of small still lifes but I want something I can process easily. For example, a csv file, or any spreadsheet format would work. There could be a column with number of cells, an RLE string for the pattern, and possibly other annotations such as common name, if any, and whether it is strict.

For my intended application, I could generate them in lifesrc and filter by symmetry, but I'd like a canonical list to avoid reinventing the wheel.

I noticed this thread and it also looks promising, but I'm not sure there's enough for me to piece it together into a complete list.

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dvgrn
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Re: Canonical list of still lifes in script-readable form?

Post by dvgrn » June 24th, 2021, 11:57 am

pcallahan wrote:
June 24th, 2021, 11:34 am
Sorry if this is something I should be able to find. I know we have carefully curated enumerations of small still lifes but I want something I can process easily. For example, a csv file, or any spreadsheet format would work. There could be a column with number of cells, an RLE string for the pattern, and possibly other annotations such as common name, if any, and whether it is strict.

For my intended application, I could generate them in lifesrc and filter by symmetry, but I'd like a canonical list to avoid reinventing the wheel.

I noticed this thread and it also looks promising, but I'm not sure there's enough for me to piece it together into a complete list.
I think your best bet is Apple Bottom's Git repository from half a decade ago -- there's a link in that thread:

https://github.com/AppleBottom/CGoL-sti ... numeration

If you need the 31-34 bit enumerations, I think they can be found later in the thread, but they're fairly bulky so it's easier not to include them unless you really need them.

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pcallahan
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Re: Canonical list of still lifes in script-readable form?

Post by pcallahan » June 24th, 2021, 1:00 pm

dvgrn wrote:
June 24th, 2021, 11:57 am
I think your best bet is Apple Bottom's Git repository from half a decade ago
Thanks! This covers the range I need. Actually, I just want to count 2x2 windows containing live cells for the purpose of laying them out as magnetic tiles. I am curious which have unique tile counts, but it's fine if I only go into the thousands of patterns, not millions or more.

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pcallahan
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Re: Canonical list of still lifes in script-readable form?

Post by pcallahan » June 25th, 2021, 2:08 pm

I was able to run my script on the list of strict still lifes. I stopped at 20 cells, though I could have gone further.

I am counting the five types of 2x2 windows up to symmetry that contain live cells, mostly in the hope of coming up with puzzles based on these tiles. I'm not sure the puzzles leverage enough human intuition to be any fun. I'm still experimenting. There may be some interesting variations.

For example, an eater can be characterized as 8⠁6⠃1⠊2⠋ (using unicode braille to indicate 2x2 windows). I.e., there are 8 windows with one cell, 6 with two orthogonal, 1 with two diagonal, and 2 with three cells. A block is 4⠁4⠃1⠛. In fact, an eater or block is the only still life up to symmetry that matches its window counts, but as patterns become larger, there is ambiguity. At 8 cells, 12⠁4⠃3⠊2⠋ matches canoe and very long snake.

Based on my script and some rough analysis with command line tools like uniq, I believe there are 272 still lifes up to 20 cells that are uniquely characterized by 2x2 window counts. Corrections welcome, as always. Here are they are listed with apgcode:

Code: Select all

xs4_252 8⠁4⠊
xs4_33 4⠁4⠃1⠛
xs5_253 7⠁2⠃3⠊1⠋
xs6_25a4 10⠁7⠊
xs6_356 6⠁4⠃2⠊2⠋
xs6_39c 10⠁4⠃2⠋
xs6_696 8⠁4⠃4⠊
xs6_bd 8⠁4⠃1⠊2⠋
xs7_178c 8⠁6⠃1⠊2⠋
xs7_2596 10⠁4⠃5⠊
xs7_25ac 9⠁2⠃6⠊1⠋
xs7_3lo 10⠁4⠃2⠊2⠋
xs8_178k8 11⠁4⠃5⠊1⠋
xs8_25ak8 12⠁10⠊
xs8_35ac 8⠁4⠃5⠊2⠋
xs8_6996 8⠁8⠃4⠊
xs8_69ic 12⠁4⠃6⠊
xs9_25a84c 13⠁4⠃6⠊1⠋
xs9_25ako 11⠁2⠃9⠊1⠋
xs10_0cp3z32 16⠁6⠃4⠋
xs10_0drz32 14⠁6⠃1⠊4⠋
xs10_178kk8 11⠁8⠃5⠊1⠋
xs10_25a8426 15⠁4⠃7⠊1⠋
xs10_3215ac 12⠁6⠃5⠊2⠋
xs10_32qr 10⠁10⠃2⠋1⠛
xs10_35ako 10⠁4⠃8⠊2⠋
xs10_4al96 12⠁4⠃10⠊
xs10_drz32 12⠁6⠃2⠊4⠋
xs10_g0s252z11 13⠁6⠃6⠊1⠋
xs10_g8ka52z01 14⠁13⠊
xs10_g8o652z01 12⠁4⠃7⠊2⠋
xs11_0cp3z65 16⠁6⠃2⠊4⠋
xs11_0drz65 14⠁6⠃3⠊4⠋
xs11_0g0s252z121 16⠁4⠃10⠊
xs11_256o8go 13⠁6⠃5⠊3⠋
xs11_25akg8o 15⠁4⠃9⠊1⠋
xs11_2ege13 12⠁10⠃3⠊2⠋
xs11_31461ac 17⠁6⠃3⠊3⠋
xs11_35a8426 14⠁6⠃6⠊2⠋
xs11_69lic 12⠁8⠃8⠊
xs11_g0s453z11 11⠁10⠃2⠊3⠋
xs11_g8ka52z11 13⠁2⠃12⠊1⠋
xs11_g8o652z11 11⠁6⠃6⠊3⠋
xs12_0g8ka52z121 16⠁16⠊
xs12_0g8o652z121 14⠁4⠃10⠊2⠋
xs12_25akg84c 17⠁4⠃10⠊1⠋
xs12_25iczw1252 18⠁4⠃11⠊
xs12_3123cko 12⠁8⠃4⠊4⠋
xs12_3215ako 14⠁6⠃8⠊2⠋
xs12_330f96 10⠁12⠃2⠊2⠋1⠛
xs12_354qic 12⠁10⠃5⠊2⠋
xs12_4alla4 12⠁6⠃12⠊
xs12_642tic 12⠁8⠃7⠊2⠋
xs12_g4q552z11 13⠁8⠃8⠊1⠋
xs12_g8ka53z11 12⠁4⠃11⠊2⠋
xs12_g8o653z11 10⠁8⠃5⠊4⠋
xs12_o4q552z01 12⠁8⠃10⠊
xs13_0g4q552z121 16⠁6⠃12⠊
xs13_0g8ka52z321 15⠁2⠃15⠊1⠋
xs13_178n96 12⠁10⠃7⠊2⠋
xs13_1no3146 18⠁10⠃1⠊4⠋
xs13_25a842ak8 20⠁4⠃12⠊
xs13_641vg4c 16⠁12⠃4⠋
xs13_c9jz39c 20⠁8⠃2⠊4⠋
xs13_ca168ozx32 19⠁8⠃4⠊3⠋
xs13_g88m96z121 14⠁8⠃11⠊
xs13_g8ge96z121 13⠁10⠃8⠊1⠋
xs13_g8ka52z56 17⠁4⠃12⠊1⠋
xs13_ggca52z65 15⠁6⠃8⠊3⠋
xs13_j5c48cz11 17⠁8⠃2⠊5⠋
xs13_j5c4goz11 19⠁8⠃1⠊5⠋
xs13_wggm96z252 16⠁8⠃10⠊
xs14_0g8ka53z321 14⠁4⠃14⠊2⠋
xs14_0g8o653z321 12⠁8⠃8⠊4⠋
xs14_25iczx115a4 20⠁6⠃12⠊
xs14_2egu156 13⠁14⠃3⠊3⠋
xs14_3123qp3 16⠁10⠃2⠊4⠋1⠛
xs14_32132qr 14⠁12⠃1⠊4⠋1⠛
xs14_33gv146 15⠁14⠃3⠋1⠛
xs14_3pczw6jo 22⠁8⠃6⠋
xs14_4a9b8ozx32 17⠁12⠃3⠊3⠋
xs14_4aab8ozx32 15⠁14⠃2⠊3⠋
xs14_64132qr 16⠁12⠃4⠋1⠛
xs14_65la4ozx11 13⠁10⠃10⠊1⠋
xs14_69ak8zx1252 18⠁6⠃13⠊
xs14_69la4ozx11 14⠁8⠃13⠊
xs14_drzrm 16⠁8⠃3⠊6⠋
xs14_g8ka52z1ac 19⠁4⠃13⠊1⠋
xs14_g8ka53z56 16⠁6⠃11⠊2⠋
xs14_ggca53z65 14⠁8⠃7⠊4⠋
xs14_j9a4zc93 21⠁8⠃5⠊3⠋
xs14_j9c826z23 21⠁8⠃2⠊5⠋
xs14_wg8ka52z2521 18⠁19⠊
xs15_02llicz252 18⠁10⠃11⠊
xs15_08o6996z321 14⠁14⠃6⠊2⠋
xs15_0bt066z65 18⠁10⠃3⠊4⠋1⠛
xs15_0g88a52z8k96 22⠁6⠃13⠊
xs15_0g8gka52z343 18⠁6⠃15⠊
xs15_0g8ka52zbc1 19⠁4⠃15⠊1⠋
xs15_0o4a52z8k96 22⠁4⠃15⠊
xs15_256o8br 15⠁12⠃4⠊3⠋1⠛
xs15_33gv1oo 14⠁16⠃2⠋2⠛
xs15_4aab88gzx311 14⠁16⠃4⠊2⠋
xs15_4aab8oz033 14⠁16⠃2⠊2⠋1⠛
xs15_4al5ak8zx11 16⠁6⠃16⠊
xs15_695q4ozw121 16⠁8⠃14⠊
xs15_699m88gzx121 14⠁12⠃11⠊
xs15_699mkk8zx1 12⠁14⠃7⠊2⠋
xs15_69ab8ozx32 17⠁14⠃3⠊3⠋
xs15_8ehegoz023 13⠁14⠃5⠊3⠋
xs15_8o652zrm 17⠁8⠃6⠊5⠋
xs15_c88b9czw33 15⠁16⠃3⠋1⠛
xs15_ck0o8brzw1 17⠁12⠃3⠊3⠋1⠛
xs15_db8oz39c 19⠁12⠃1⠊5⠋
xs15_g8o6996z121 13⠁14⠃8⠊1⠋
xs15_w8ka952z2521 20⠁6⠃14⠊
xs15_wg8ka52z6521 17⠁2⠃18⠊1⠋
xs15_wggm96z696 16⠁12⠃10⠊
xs15_woka52zdb 17⠁6⠃11⠊3⠋
xs16_0g8gka53z343 17⠁8⠃14⠊1⠋
xs16_0g8ka52z3kp 21⠁4⠃16⠊1⠋
xs16_0g8ka53zbc1 18⠁6⠃14⠊2⠋
xs16_252s0ccz2521 20⠁10⠃10⠊1⠛
xs16_32qb8og4c 18⠁14⠃6⠋
xs16_356o8br 14⠁14⠃3⠊4⠋1⠛
xs16_4aab88czx33 14⠁18⠃2⠊2⠋1⠛
xs16_4s0v1e8zw11 12⠁18⠃2⠊4⠋
xs16_4s3iak8zw121 16⠁8⠃13⠊2⠋
xs16_5bo3146z32 25⠁10⠃2⠊5⠋
xs16_69960uic 14⠁16⠃6⠊2⠋
xs16_8o1vg4cz23 17⠁16⠃5⠋
xs16_8o653zrm 16⠁10⠃5⠊6⠋
xs16_g88a52zg9icz01 24⠁6⠃14⠊
xs16_g88m996z1221 12⠁16⠃10⠊
xs16_gjlkk8z146 17⠁16⠃3⠊3⠋
xs16_wg8ka53z6521 16⠁4⠃17⠊2⠋
xs16_xg8ka52z4a521 20⠁22⠊
xs17_02llicz696 18⠁14⠃11⠊
xs17_03jgf9z2521 17⠁12⠃7⠊3⠋1⠛
xs17_03pcz6iq23 22⠁14⠃6⠋
xs17_0gjlkk8z1226 16⠁18⠃5⠊2⠋
xs17_252s0cczw39c 21⠁12⠃5⠊3⠋1⠛
xs17_25a4ozx1259a4 22⠁6⠃17⠊
xs17_3jgf96z121 15⠁14⠃6⠊3⠋1⠛
xs17_4aabkkozx32 13⠁16⠃7⠊3⠋
xs17_4aaraar 14⠁16⠃2⠊6⠋
xs17_4al5q4ozx121 16⠁8⠃18⠊
xs17_4aq3og4cz32 25⠁12⠃2⠊5⠋
xs17_5b88brzx32 19⠁16⠃2⠊3⠋1⠛
xs17_6a88brz033 16⠁18⠃1⠊2⠋2⠛
xs17_6ao8brz32 19⠁14⠃1⠊5⠋1⠛
xs17_8e1t2sgzw23 15⠁18⠃4⠊3⠋
xs17_8o1vg33z23 16⠁18⠃4⠋1⠛
xs17_9f0s2sgzw23 16⠁18⠃2⠊4⠋
xs17_bdggzw125ak8 19⠁6⠃14⠊3⠋
xs17_c88bb8ozw33 14⠁20⠃2⠋2⠛
xs17_c9baaczw33 14⠁18⠃1⠊4⠋1⠛
xs17_c9jz3pczw23 26⠁10⠃2⠊6⠋
xs17_dj8gzw125ak8 21⠁4⠃18⠊1⠋
xs17_ggca52zmdz11 19⠁8⠃9⠊5⠋
xs17_gs2qb8ozx32 15⠁18⠃1⠊5⠋
xs17_xg4q552z4a521 20⠁6⠃18⠊
xs17_xg8ka52zca521 19⠁2⠃21⠊1⠋
xs17_xg8o652zca611 15⠁10⠃9⠊5⠋
xs18_03jgf9z6521 16⠁14⠃6⠊4⠋1⠛
xs18_04ap3z4a43033 22⠁12⠃8⠊2⠋1⠛
xs18_0gbb8o652z121 20⠁12⠃9⠊2⠋1⠛
xs18_0ggcil96z1243 18⠁12⠃15⠊
xs18_0gilla4z34a4 20⠁12⠃14⠊
xs18_0gillicz1226 17⠁18⠃8⠊1⠋
xs18_0j5q4oz34521 17⠁10⠃16⠊1⠋
xs18_0mllicz346 16⠁18⠃7⠊2⠋
xs18_178bb8ozw33 16⠁20⠃1⠊2⠋2⠛
xs18_25a88brzw33 19⠁16⠃5⠊1⠋2⠛
xs18_25ak8gzy0125ak8 22⠁25⠊
xs18_3jgf96z321 14⠁16⠃5⠊4⠋1⠛
xs18_3pczw6jozx146 28⠁10⠃8⠋
xs18_4aabaaczx33 13⠁20⠃3⠊3⠋1⠛
xs18_5b88brz033 18⠁18⠃2⠊2⠋2⠛
xs18_628c1f83146 26⠁14⠃6⠋
xs18_69bkk8z653 15⠁14⠃10⠊3⠋
xs18_69n8brzx11 14⠁16⠃8⠊2⠋1⠛
xs18_8u1vg4cz23 16⠁18⠃1⠊6⠋
xs18_bt066zrm 20⠁12⠃3⠊6⠋1⠛
xs18_cc0si52z4a43 22⠁10⠃10⠊2⠋1⠛
xs18_cidicggzx343 15⠁14⠃13⠊1⠋
xs18_cillicz066 16⠁18⠃8⠊1⠛
xs18_dj8gzw125ako 20⠁6⠃17⠊2⠋
xs18_drzrmz65 20⠁10⠃4⠊8⠋
xs18_g84q5icz12521 20⠁6⠃20⠊
xs18_gg0gbdz110nq 19⠁14⠃3⠊5⠋1⠛
xs18_ggca53zmdz11 18⠁10⠃8⠊6⠋
xs18_gjlkkoz1226 14⠁20⠃3⠊4⠋
xs18_wcc0s252z4a511 22⠁12⠃11⠊1⠛
xs18_wg8ka51246z2521 23⠁4⠃19⠊1⠋
xs18_xg4q552zca521 19⠁8⠃17⠊1⠋
xs18_xg8ka53zca521 18⠁4⠃20⠊2⠋
xs18_xg8o653zca611 14⠁12⠃8⠊6⠋
xs19_025icz66079k8 24⠁10⠃11⠊2⠋1⠛
xs19_03jgf96z2521 17⠁14⠃9⠊3⠋1⠛
xs19_06996z311d93 19⠁20⠃4⠊3⠋
xs19_09v0rrz65 20⠁16⠃2⠊4⠋2⠛
xs19_0ggcil96z3443 16⠁16⠃14⠊
xs19_255q4gzy0125ak8 22⠁6⠃21⠊
xs19_256o8go8br 19⠁14⠃5⠊5⠋1⠛
xs19_259ak8zy0125ak8 24⠁6⠃20⠊
xs19_25ak8gzy0125ako 21⠁2⠃24⠊1⠋
xs19_25akozwcc0f9 19⠁12⠃10⠊3⠋1⠛
xs19_3iabaaczw113 15⠁20⠃3⠊5⠋
xs19_3pc0c4goz0c93 29⠁12⠃1⠊7⠋
xs19_3pc0cczw123146 26⠁12⠃2⠊6⠋1⠛
xs19_6413or2pm 26⠁14⠃3⠊4⠋1⠛
xs19_642hv0rr 19⠁18⠃2⠊3⠋2⠛
xs19_696o696zw343 20⠁14⠃14⠊
xs19_699mkkozx56 14⠁18⠃7⠊4⠋
xs19_69abaaczx33 15⠁20⠃4⠊3⠋1⠛
xs19_8u1rq23z23 16⠁18⠃1⠊6⠋1⠛
xs19_8u1t2sgz0123 14⠁20⠃5⠊4⠋
xs19_8u1vg33z23 15⠁20⠃1⠊5⠋1⠛
xs19_9f0s4zw230f9 18⠁20⠃6⠋
xs19_9f0v1oozw23 16⠁22⠃4⠋1⠛
xs19_c9b88gz39d11 20⠁20⠃2⠊4⠋
xs19_c9bq23z39c 23⠁16⠃7⠋
xs19_g88cila4z1253 18⠁10⠃16⠊2⠋
xs19_rb88brz023 19⠁20⠃3⠋2⠛
xs19_rdzmrzw352 21⠁10⠃7⠊7⠋
xs19_w4alla4z2553 17⠁12⠃16⠊1⠋
xs19_woka52zdrz32 21⠁8⠃12⠊5⠋
xs19_xg8ka5123z4a521 23⠁4⠃21⠊1⠋
xs19_xg8kc3213z4a521 21⠁6⠃17⠊3⠋
xs20_03j0v1ooz2521 21⠁16⠃8⠊1⠋2⠛
xs20_03jgf96z6521 16⠁16⠃8⠊4⠋1⠛
xs20_06996z311d552 18⠁22⠃6⠊2⠋
xs20_069bkk8z3553 15⠁18⠃10⠊3⠋
xs20_0c9b88gz255d11 19⠁22⠃4⠊3⠋
xs20_0g4q5la4z34521 20⠁10⠃20⠊
xs20_0gbbo8brz121 21⠁16⠃5⠊3⠋2⠛
xs20_0giligz122qi43 23⠁18⠃9⠊1⠋
xs20_255q4gzy0125ako 21⠁8⠃20⠊1⠋
xs20_356o8go8br 18⠁16⠃4⠊6⠋1⠛
xs20_35ak8gzy0125ako 20⠁4⠃23⠊2⠋
xs20_35akozwcc0f9 18⠁14⠃9⠊4⠋1⠛
xs20_3pe0okczwdb 19⠁14⠃6⠊7⠋
xs20_4alligzx4aa52 20⠁14⠃16⠊
xs20_5bo3qp3z32 27⠁14⠃3⠊5⠋1⠛
xs20_695q4ozca521 19⠁10⠃19⠊1⠋
xs20_69fgciiczw23 15⠁20⠃8⠊3⠋
xs20_69mggm96zw66 20⠁18⠃10⠊1⠛
xs20_8kkbaaczx356 14⠁18⠃9⠊4⠋
xs20_c4go3dg628czy111 30⠁14⠃2⠊6⠋
xs20_c88bbgz39d11 19⠁22⠃2⠊3⠋1⠛
xs20_c93g08oz33039c 30⠁14⠃6⠋1⠛
xs20_c93ggoz311oi6 28⠁16⠃1⠊6⠋
xs20_c9b88brzw33 19⠁22⠃3⠋2⠛
xs20_caabqicz33 15⠁20⠃3⠊5⠋1⠛
xs20_cc0v1qrzw23 17⠁22⠃1⠊3⠋2⠛
xs20_cillicz4aa4 20⠁18⠃12⠊
xs20_cim88brzx311 15⠁20⠃6⠊3⠋1⠛
xs20_cq231eoz012311 16⠁16⠃4⠊8⠋
xs20_g39cz11d5h3zx11 26⠁18⠃6⠋
xs20_g88b94oz129d11 22⠁20⠃6⠊2⠋
xs20_ggmllicz1226 15⠁22⠃6⠊3⠋
xs20_mm0u1qrz101 22⠁18⠃4⠊2⠋2⠛
xs20_o8baab8ozx33 16⠁24⠃4⠋1⠛
xs20_o8bb8oz011dd 14⠁24⠃2⠊2⠋2⠛
xs20_o8gehegozw343 16⠁20⠃9⠊2⠋
xs20_oe1raarz011 17⠁18⠃3⠊7⠋
xs20_rdzmrzw356 20⠁12⠃6⠊8⠋
xs20_woka53zdrz32 20⠁10⠃11⠊6⠋
xs20_xg8ka5123zca521 22⠁6⠃20⠊2⠋
xs20_xg8ka51246z4a521 25⠁4⠃22⠊1⠋
xs20_y1g8ka52zg8ka521z01 24⠁28⠊
Viewable pattern:

Code: Select all

x = 165, y = 195, rule = B3/S23
58b2o5bo6bo17bo$16bo9b2o3bo3b2o4b2o4bo5b2o4bo4bobo4bobo4b2o3b2o4bobo$b
o8bo4bobo3b2o4bo2bobo3bo3bobo3bobo3bobo3bo4bobo4bobo4bobo2bo2bo2bo2bo$
obo2b2o2bobo2bobo3bobo2bo4bobo2bo4bo4bo2bo2bobo3bo5bo5bobo4bobo3bo2bo
2bobo$bo3b2o3b2o3bo4b2o3b2o4bo3b2o2b2o5b2o4bo4b2o3b2o6bo5b2o5b2o4bo3$
99b2o4b2o$15b2o4b2o48b2o26bo5bo5bo$15bo5bo49bo3b2o7bo7bo7bo5bo3bobo$
11b2o4bo5bo5b2o22b2o5b2o4bo5bo2bobo5bobo5bobo7bo5bo3bobo$2b2obo4bobo3b
2o4b2o4bo2bo4b2o9b2o4b2o4bobo3bobo3b2o4bo6bobo5b2o6b2o4b2o5bo$bo2b2o3b
obo4bo5bo4bob2o4bo2bobo5bobo9bobo3bobobo2bo5bobo5bobo6b2o4bo5bo6bobo$o
bo5bobo7bo4bo3bo6bobo2b2o2b2o2bo3b4o2bobo5bo2bo3bo5bobo5bobo5bobo5bo4b
o6bobo$bo7bo7b2o3b2o2b2o7bo7bob2o4bo2bo2b2o7b2o3b2o6bo7bo7bo5b2o3b2o7b
o3$107bo$76bo8bo20bobo$51b2o6b2o6b2o6bobo6bobo18bobo$3bob2o5b2obo4bo
25b2o3bobo5bobo5bobo6bobo6bobo8b2o7bo10b2o7b2o13b2o$3b2obo4bo2b2o3bobo
9b2o4b2o6bo2bo4bo6bobo5b2o7bobo6b2o7bo2bobo5bo8bobo6bobo5b2o6bobo$b2o
7bobo6bobo6b2o2bo3bo2bobo2bobobo4b3o5bobo6b2o6bobo7b2o4bobo2b2o3bobo8b
2o6bobo6bobo3b2o2bo$obo6bobo6b2obobo2bo2bobo3bobo2b2o2bo2bo8bo5bobo5bo
bo6bobo6bobo2bobo7bobo5bob2o5b2o2bo4b2obobo2bo2b2o$bo8bo11b2o2b2o2bo4b
2o8b2o8b2o6bo7bo8bo8bo4bo9bo6b2obo5bob2o5b2ob2o3b2o3$104b2o$105bo26b2o
$49bo7b2o44bo7b2o4bo7bo7bo$16b2o6b2o6b2o7bo6bobo6bobo43b2o6bo4bobo5bob
o5bo$2b2o7b2o3bobo5bobo5bobo5bobo6bobo6bobo8bo5b2o13bo6b2o6bo7bo2bo2bo
4bobo5bobo$bo2bo6bobo4bo6bobo5b2o5bobo8bo7bobo6bobo5bo8b2o2bobo5bo2bo
2b2o3b2o2b2o3b2obo4bob2o4bobo$ob2obo2b2obobo3bob2o5bobo6b2o4bob2o5bob
2o6bobo4bobobo3bo3b2o3bo2bo2bo3b2obob2o2bo4bo2bo7bobo5bobo4bobo$bo2bo
3bobobo5bo2bo5bobo5bobo4bo2bo5bo2bo6bobo3bobobo3bobo2bo2bobo2b2o4bo2bo
7bo3bobo7bobo5bobo5bobo$2b2o7bo7b2o7b2o6b2o5b2o7b2o8bo3b2ob2o3b2ob2o5b
o11b2o6b2o4bo9bo7bo7bo3$100b2o$57bo43bo$2o23bo30bobo40bo42bo$o23bobo6b
2o7b2o13bo41b2o6b2o6b2o24bobo$bo6b2o6b2o7bo7bobo6bobo9b3o43bo6bo7bo16b
2o6bobo$2o6bo7bo3b2o4b3o5bobo6bobo7bo9b2o9b2o8b2o4b2o6bo10bo7bo7b2o4bo
2bo5bo$2b2o6bob2o4bo2bo7bo5bobo6b2o8bo7bobo9b2o8b2o5bo6b2o5b5o3b5o7b2o
5bobo3b2obo$2bobo4b3obo3b3o8bobo5bobo7b2o4bobo7bobob2o23bob2o4bo4bo7bo
7b2o7b3obo3bo2bo$3bobo2bo7bo11bobo6bobo6bobo2bobo7b2obo2bo2bob3obo2b2o
b4o2b2obo2bo2bo7bobo5b3o4bo2b4o2bo2bo4bobo$4bo3b2o6b2o11bo8b2o7b2o3bo
12b2o3b2obob2o2bob2o2bo2b2ob2o4b2o7b2o7bo6b2o2bo3b2o6bo3$8b2o76bo27bo$
8bo4b2o21b2o47bobo16b2o7bobo$9bo4bo5b2o6b2o6bo14bo9bo15b2o7bobo6bo9bo
8bobo$8b2o3bo7bo6bo9bo3b2o6bobo7bobo5b2o7bo10bo5bobo7bo11bo$3b2o3bo3bo
7bo8bo7b2o4bo7bobo7bo6bobo7bo8bo6bobo7bobo8bo$2bo2bo3bo2bobo5bobo5b2o
6bo5bo9bobo7b3o5bo8bo6bo8bob2o6bobo6bo9bo2bo4b2ob2o$bobobo2b2o3bobo5bo
bo6b2o5b2o4b3o7bobo9bo3b2ob2o4b2o7b3o6bo2bo6bobo5bobo7b4o5bob2o$obobo
3bo5bobo5bobo5bobo6bo4bo2bo6bobo5b2obo5bo2bo4bob2o7bo7bobo6bobo5bobo4b
2o9bo$o2bo5bo5bobo5bobo5bobo2bobo3bo3b2o7bobo3bo2bo6bo2bo3bo2b2o6bobo
7bobo6bobo5bobo2bobo2b2o2b2obo$b2o5b2o6bo7b2o6b2o2b2o4b2o12bo5b2o8b2o
4b2o10bo9bo8bo7bo4bo3b2o2b2ob2o3$68b2o$68bo24b2o33bo7b2o$69bo24bo13bo
8b2o8bobo6bo$3bo6b2o17bo8bo16b2o4b2o5b2o7b2o13bo6bo7bobo7bobo7bobo7bo$
3b3o4b2o8b2o6bobo6bobo6bo8bo6bo5bo8b2o6bo6b2o4bobo7bobo7bobo7bo7b2o$6b
o7bo4bo2bo6bobo5bo2bo5b3o8bo4bob2o3bo14bobo2bo5bo2bobo9bo8bobo7b3o6b2o
$b5o4b5o3bo2bobo3bobobo3b2ob2o4b2o3bo3b5o2b2obobo2b2o5b6o2bo2b4o2b4o3b
2ob2o5bob2o7bobo9bo5bobo$o8bo7bob2obo3bobobo3bo2bo5bo2b3o3bo8bobo6b2o
3bo4bo2b2o7bo8bo2bo5bo2bo7bobo7bobo5bobo$b3o6b3o5bo2bo4bo2bo4bo2bo5bo
2bo5bob2o5bobo6bobo5bo9b2o3bo7bo2bo6bo2bo7bobo6bobo6bobo$3bo8bo6b2o6b
2o6b2o7b2o7bobo6bo8bo6b2o8b2o2b2o8b2o8b2o9bo8bo8bo3$120bo$11b2o99b2o5b
obo$12bo6b2o91bo7bobo$bo9bo8bo8bo83bo8bo14b2o5b2o$obo7bo8bo8bobo29b2o
16bo5b2o17b2o7b2o7bo6b2o8bo5bobo$obo7bobo6bobo7bobo28b2o6b2o7bobo4bo
19bo7bo7bo6bo2bo5bo8bobo$bob2o6bobo6bobo8bo7bo2b2o7bo2bo12bobo6bobobo
5bo11b2o4bob2o5bo5bo7bo2bo5b5o5bobo$2bo2bo6bobo6bobo7bob2o4b4o2bo5b4o
3b6o3bobob2o3bo2bobo3b2o7b2o2bobo2b2obo2bo2b2o6b3o5b2ob2o8bo5bobo$4bob
o6bobo6bobo4bobob2o9b2o3b2o6bo5bo2b2obobo3b2o3bo3bo4b2o2bo2bobobo5bob
2o4b2o7bo6bo2bo4b3o7bobo$5bobo6bobo6bobo2bobo6b4o7bobo2b2o3b3o8bobo5b
3o5bobo2bo2bo2bob2o6bo7bobo5bobo5bo2bo3bo11bobo$6b2o7bo8b2o3bo7bo2bo7b
2o3b2o5bo8b2o6bo6b2ob2o5b2o9b2o8b2o6bo7b2o4b2o11b2o3$28b2o$bo10bo16bo
16b2o10b2o$obo8bobo6bo6bo9bo9bo9bo2bo$bobo7bobo5bobo5b5o3b3o7bo10bo2bo
4bo9b2o17bo4b2o11b2o4b2o5b2o8b2o5b2o$2bobo7bo7bobo8bo2bo10b2o8bob2o4bo
bo8bo17bobo3bo12bo5b2o5bo10bo6bo$3bobo7b3o5b2o6bo5b5o6bo9bo7b2o9b3o5bo
2bo4bobobo4bob2o9bo7bo4bo2bo5bob2o3bob2o$4bobo9bo6b2o4b2o9bo5bob2o4bob
o9b2o4b3o2bo3b6o3bo2bobo3b2obo2bo3b5o3b5o3b5o2b2obobo3b2obo$5bobo5b2ob
o6bo6bo6b3o4bobob2o3bobo10bobo2bo3b2o3bo8bob2obo3bo5b2o2bo7bo7bo8bobob
o6bo$6bobo3bo2bo4b2obo4bo7bo6bobo6bobo8b2obobo3b3o6b6o3bo2bo5b3o7bo2b
2o2b2o2b2o2b2o2b2o3bo2bo7bob2o$7bo5b2o5b2ob2o3b2o6b2o6bo8bo9b2ob2o6bo
8bo2bo4b2o8bo6b2o2b2o6b2o6b2o4b2o7b2ob2o3$38b2o$39bo12b2o$15bo21bo10bo
3bo$14bobo20b2o8bobo3bo16bo9b2o9b2o18bo30bo$13bobo22bo7bobo3b2o15bobo
8bobo8bobo8b2o6bobo19bo8bobo8bo$2b2o8bobo6b2o7b2o4bo8bobo4bo10b2o5bobo
8bobo8b2o8bobo6bobob2o3bo10bobo6bobo7b3o$3bo7bobo7b2o7b2o4b2o6bobo6bo
9bo7bobo8bobo9b2o7bobo7bob2o2bobo8bo2bo6bo8bo$3bob2o4b2o12bo12bo4bobo
6b2o6b2obo2bo5bobo8bobo8bobo7b2o7bo6bo3bo6b2ob2o5b4o5b5o$2obobo3b2o8b
7o2b6o2b2o4bobo9b2o5bob4o7bo9bobo8b2o9b2o4b2o7b4o8bo2bo8bo9bo$bobobo4b
o8bo8bo4bo2bo5bo11bobo4bo11bob2o8bobo9b2o7bo4bo13b2o6bobobo5b2obo5b2ob
o$bo2bo4bo12b2o6b3o5bo4bo11bobo4b3o9bo2bo8bobo8bobo3b2obo5bobo6b2o2bob
o6bo2bo4bo2bo5bo2bo$2o7b2o11b2o5b2o6b2o3b2o12bo7bo10b2o10bo10bo4b2ob2o
5b2o6b2o3bo8b2o6b2o7b2o3$58b2o$59bo$57bo$42bo14b2o58b2o$41bobo14bo58bo
7bo$b2o6b2o29bobo13bo35b2o24bo5bobo10bo5b2o$o2bo4bobo7b2o7b2o10bobo4b
2o8b2o7b2o5b2o18bobo13b2o7b2o6bobo8bobo4b2o$obobo3bo9b2o7b2o9bobo5bobo
8bo7b2o5b2o19b2o8b2o4bo7bo9bo8bobo$bobobo3b4o9bo8bo5bobo7b2o6bo20bo18b
2o5bo2bo3bob2o5bo8b2o5bobob2o3b4o$3bobo7bo4b5o4b5o4bobo10b2o4b2o6b6o3b
5o4b2ob2o7b2o2bo3bob3o2b2obo2bo2b2o5b2obo5bobobo4bo4bo$2bobo4b3obo3bo
8bo8bobo11bobo4bo5bo5bo2bo7bo2bobo3b2o2bo2b2o3bobo6bobob2o3bob2o2b2obo
bo3bobobo4bob2obo$bobo5bo2bo4bob2o4bobo2b2o2bobo9b2obobo2bo8b5o4bo2b2o
2b2o3bobo2bo2bobo5bobob2o3bobo5bo2b2o6bobo3bobo6bo2bo$b2o7b2o4b2ob2o5b
o3b2o3bo10b2ob2o3b2o9bo5b2o2b2o6b2ob2o5b2o6b2ob2o4b2o5b2o10bo5bo8b2o3$
10b2o$10bo$11bo19b2o$6b2o2b2o14b2o3bo77bo46bo$5bobo2bo16bo4bo15bo22b2o
9b2o9b2o13bobo14b2o28bobo$4bobo4bo4bo9bo4b2o9bo4bobo9bo11bobo8bobo8bob
o8b2obobo4bo10bo4b2o7b2o13bobo$3bobo4b2o3bobo8b2o3bo8b3o5bo9bobo11bobo
8bobo8b2o8b2obo5bobo6bo4bo2bo7bo2bo11bobo$2bobo5bo3bobobo4b2obo5bo6bo
9b3o7bobo11bobo8bobo9b2o9b2o5bobo5b6o3bo6bo2bo10bobo$bobo7bo2bo2bobo3b
2obo4b2o6b6o7bo7bobo11bobo8bobo8bobo8bo7b2o15bob2o3b2ob2o7bobo$obo7b2o
3bobo2bo6b2o4b2o9bo4b2obo8bobo12bo9bobo8b2o9bo8b2o5b2o5b2ob2o5bo2bo6bo
$o9bo5bobobo7bo4bobo5b3o5b2obobo7bobo2b2o6bob2o8bobo9b2o5bobo8bobo3bo
2bo5bo8bobobo3b2obo$bo9bo5bobo7bo6bobo3bo12bobo7bo2bobo7bo2bo8bobo8bob
o3bobo6b2obobo3bo2bo5bob2o6bo2bo2bo2bo$2o8b2o6bo8b2o6b2o3b2o12bo9b2o
11b2o10b2o9b2o4bo7b2ob2o5b2o5b2ob2o7b2o4b2o3$20bo11b2o$19bobo9bobo4b2o
b2o12b2o97b2o$18bobo9bobo5b2obo13bo14b2o26bo8b2o45bo$17bobo9bobo9bo7bo
7bo9b2o2bo25bobo8bo7b2o4b2o9b2o5b2o9b2obo5b2o$16bobo9bobo10b2o4b3o6b2o
8bob2o27bobo7bo8b2o5bo8bobo6bo10bob2o5bo$3bob2o2bo6bo10bobo9b2o5bo8bo
4b2o3bo12b2ob2o5b2ob2o5bo8b4o12bob2o5bobob2o3bob2o7bo8bob2o$3b2ob4o4b
2obo8bobo9bobo6b5o3b2obo2bo3b2ob2o8b2obo7bob2o3bobobo4b2o3bo3b6o2b2ob
2o4b2obobo3b2obo5b2obo5b2obob2o$b2o10bo2bo8bobo9bobo11bo4bob2o6bob2o4b
2o6bo2b2o2bo5bobobobo2bo2b3o3bo5bo3bo8bobobo4bobo6bob2o5bobo$obo5b2o2b
o2bo8bobo9bobo6b6o3bo9bo9bo2bob2obo2bobobob2o2bobobobo2bo2bo5bob4o4bob
4o3bo2bo5bobob2o3bo8bobo$bo6b2o3b2o10bo11bo7bo2bo5b2o8b2o10b2obobo6b2o
b2o3bo3bo4b2o7bobo7b2o2bo4b2o7b2ob2o2b2o7b2ob2o3$37bo$36bobo12b2o$36b
2o13bo$34b2o16bo102b2o$b2o6b2o24bo15b2o8bo12bo33bo17bo28bo$2bo7bo7bo
15bo7b2o7bo8bobo10bobo11bo8b2o10b3o4b2o7b3o6b2o22bo$o7bo8bobo7b2o5b2o
5bo2bo7bo8bobo10bobo9bobo7bobo6bo5bo2bo2bo5bo8bo2bo7bo9b4obo$5o3b2o6bo
b2o8bo6bo6b3o6b2o9bobo10bobo9bobo7bobo5b6o3b4o6b5o3bobobo5bobo7bo5bo$
5bo5bo4bo3b2o4bo4bo2bo10b2o6b2o8bobo10bobo9bobob2o4b2o18b2o9bo3bobobo
5bo2bo2bo3b5o$5o3b4o5b3o2bo3b6o2b2o8bo2bo5bobo8bobo10bobo10bob2o6b2o5b
2o7b2o2bo3b5o6bo2bo5b6o$o7bo10bobobo11bo7bob2obo5bobo8bobo10b2o10bo9bo
bo3bo2bo5bo2b2o4bo9bob2obo15bo$2bo7b4o6bobo3b2o2b2o2bo9bo2bo7bobo8bo2b
2o9b2obo3b2obo6b2obobo3bo2bo5bobo8bo8bo2bo5b2o2b2o4bobo$b2o6b2o2bo7bo
4b2o2b2o2b2o9b2o9bo10b2obo9bob2o3b2ob2o5b2ob2o5b2o7b2o7b2o9b2o6b2o2b2o
5bo3$8b2o22b2o109b2o$7bobo21bobo4b2ob2o4b2o9b2o13b2o49b2o9b2o6bo$6bobo
21bobo5b2obo5bo9bo2bo12bobo17b2o10b2o18bo10bo8bo$5bobo21bobo9bo6bo9b2o
bo2b2o8bobo6b2o8b2o9bobo16bo7b2obo5bo3b2o4b2o5b2o$4bobo21bobo10b2o4b2o
11bo3bo10bobo6bo19b2o9b2o6b5o3b2ob2o4b3o7b2o5b2o$3bobo9bob2o2bo5bobo9b
2o5bo2b2o5b4o6bob2o6bobo5bob2o5b4o5b2o8b2o2bo11bo5bo2bo5b3o8bo6b2o$3bo
11b2ob4o4bobo9bobo5b2obobo3bo9b2ob2o4bobobo3b2obo2bo3bo4bo3bo2b4o2bo2b
obo3b2o2b5o3b2o3b2o2b2o3bo2b7o2b5obo$b2obo8b2o10bobo9bobo7bo2b2o2bob2o
6bo8bobobo3bobobo2bo2bobo2bobo3b2o3bo2b2o3bobo2bo2bo7bo8bo7bo8bo5bo$o
2bo8bobo5b2o2bobo9bobo6bobo7bo2bo6bob2obo2bo2bo4bobo2b2o3bobo2bobo5b3o
7bo2b2o7b2o5bo8bo7bo2b2o3b5o$b2o9b2o6b2o2b2o10b2o7b2o9b2o6b2obob2o3b2o
6b2o8bo4bo6bo9b2o10b2o4b2o7b2o6b2o2b2o5bo3$110b2o$109bobo2b2o$38b2o69b
2o3bo36bo$39bo67b2o6bo34bobo$10b2o25bo7b2o36b2o23bo5b2o7b2o12bo13bobo$
9bo2bo24b2o7bo8bo27b2o6bo15bo6bo8bobo10bobo13bobo$2b2o6b2o8bo7b2o10bo
3bo8b3o17b2o15bobo14b2o6bo8bobo10bobo13bobo$3bo16b3o4bob3o3b6o2bob4o3b
o8bobo9b2o6b4o5bobo6b2o7bo5b2o9bobo10bobo13bobo$3bob2o3b4o4b2o3bo3bo4b
o2bo7bo5bo2b6o3b2obob2o2bo6bo2bo4bo2bobobob2o2bo2bo2bo2bo8b2o8bobo10bo
bo13bobo$2obob2o2bo4bo2bo2b4o2b2o3b2o4b2o5b4obo8bo5bob2o2b8o2b6o2b2obo
bobo2b2ob4o2b2o7bobo8bobo10bobo13bobo$2obo5bob2obo2bobo6bo4bo6bo9bo5b
3obo2b2obo26bobo5bo8bo8bobo8bobo10bobo2b2o9bobo$3bob2o3bo2bo4b2o2b2o3b
3obo4bo9bo7bo2bo3b2obob2o4b4o6b2o7bobo5bob4o2bo10bobo8bo2b2o8bo2bobo
10bobo$3b2obo4b2o9b2o5b2o5b2o8b2o7b2o8bobo4bo2bo6b2o8bo7b2o2bo2b2o10b
2o9b2obo9b2o14bo!
At the other end of the spectrum, 22⠁14⠃7⠊4⠋ corresponds to 2309 19-cell patterns, some of which are:

Code: Select all

x = 46, y = 49, rule = B3/S23
9b2o$9bo$2o8b3o6b2o$bo11bo4bo2bo7b2o$o11b2o4bob2o3b2o2bo4b2o2bo$obo9bo
4b2obo4bobobo4bo2bobo$b4o8bo7bo6bob2o4b2obo$5bo8bo7bo7bo8b2o$3bo2bo5bo
bo5bobo5bobo8bo$2bob2o5bobo5bobo5bobo6b2obo$2bo8bo7bo7bo7bo2bo$b2o7b2o
6b2o6b2o8b2o4$2o8b2o6b2o$o2bo7bo7bo$b3o6bo7bo7b2o8b2o$6bo2bo8bobo6bo3b
o4bobo$3b4o3b3o6bobo5bob3o6bo$3bo8bo8bo6bo9b2o$4bo7bob2o4bob2o6b4o7bo$
2bobo6b2o2bo4bobo5bobo2bo4b3obo$bobo6bo2bo5b2o2bo3bobo7bo2bo2bo$2bo8b
2o9b2o4bo9b2o2b2o3$b2o$2bo15b2o7bobo$bo7b2o7bo8b2obo4b2o$bobo2bo2bo2bo
2bo3b3o2bo5bo4bo2bo$2b5o3b6o5b4o5b2o4b3o$32bo$4bo7b2o7b2o7b3o5b3o$3bob
o5bo2bo5bo2bo5bo7bo3bo$2bo2bo4bo2bo5bo2bo5bo2b2o3bobobo$3b2o6b2o7b2o7b
2obo4b2ob2o3$39bo$30bo8b3o$b2o8b2o9b2o6b3o9bo$bobo7bobo7bo2bo8bo7bo$3b
o9bo8bobo7bo9b3o$3b2o8b2o2bo5b2ob2o4b4o9bo$6b2o8bobo7bo9bo7bo$3b2obobo
4b2obobo4b2obo5b2obo8b2o$2bobobobo3bobob2o4bobob2o3bobob2o3bob2o$3bo3b
o5bo9bo8bo7b2obo!
I don't have a clear idea of what makes a particular window count likely to be unique or ambiguous. In fact, I had expected to see all window counts being ambiguous after a certain size, but they're not. Long barges and similar patterns appear to have unique counts no matter how large they get (I haven't tried to prove this). The ones with 22⠁14⠃7⠊4⠋ have a variety of shapes, again counter to my intuition. I thought there would be an obvious family of patterns, e.g. with hooks that could be switched like the canoe and very long snake. There may yet be more commonality than I see.

So, as for puzzles, my idea was simply to start with a particular window count and ask how to realize it manually with the aid of movable tiles. However, when I start with any pattern I don't know already, I have very little idea where to start. I think it's possible to build up an idea of how the 3-cell windows can be used in hooks. If a 4-cell window occurs, of course that's a giveaway that you need a block. I also think it makes sense to leave the 1-cell windows for the end, as they are pretty easy to place after placing the others.

I have found that just placing still lifes freehand is not too hard. E.g.:
20210625_110146.jpg
20210625_110146.jpg (145.98 KiB) Viewed 982 times
As I've described before, the tiles are marked in such a way that it is easy to identify cells that are about to die or be born. In this case, I started out with a particular window count as a goal, but I would have found it nearly impossible to match it exactly, so I added some additional tiles. Maybe a puzzle that relaxed the constraint a little and allowed additional tiles is more reasonable. I also have some ideas about making a 2-player scrabble-like game that could award points for using up particular counts of tiles.

Open questions: Can this be turned into a fun puzzle? (Fun being very subjective.) How about fun for a very casual participant with limited interest in CGOL?

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pcallahan
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Re: Canonical list of still lifes in script-readable form?

Post by pcallahan » July 6th, 2021, 10:58 pm

As stated above, my goal is to come up with an engaging game or puzzle using tiles shown. It would be based on applying the CGOL still-life rule, so either 2 or 3 red edges per node, and no set of exactly three diamonds touching each other (but needless to say, the same tiles would work for other Moore neighborhood rules).

The following images show all strict still lifes up to 10 cells laid out with tiles. One visible feature is the shape of overcrowded neighborhoods. Some are visually interesting (at least to me) such as the relationship between the pool and mango, each with four cells crowded by four neighbors, the latter skewed by the displacement of upper and lower half.

One puzzle is to build a still life exhibiting a particular set of overcrowded neighborhoods. There are few enough small patterns (56 still lifes up to 10 cells) that you could just memorize solutions. However, being able to do it fast could be the basis of a 2-player game consisting of tiles chosen randomly as in Scrabble, and a deck of cards with small puzzles. The goal would be to build patterns with tiles. They would have to be still lifes to count, and they could be scored either by counting features (cells and starvation neighborhoods) or with extra points for building one that matches a card you selected. (It would take some play testing to determine if anything like this would be fun.)

Still lifes with 4 to 7 cells:
sheet1.png
sheet1.png (1.06 MiB) Viewed 856 times
Still lifes with 8 or 9 cells:
sheet2.png
sheet2.png (1.4 MiB) Viewed 856 times
Still lifes with 10 cells
sheet3.png
sheet3.png (2.13 MiB) Viewed 856 times

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dvgrn
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Re: Canonical list of still lifes in script-readable form?

Post by dvgrn » July 7th, 2021, 9:20 am

Maybe instead of cards with puzzles on them, there could be larger conglomerations of tiles that have to be completed to make a still life? What's the most improbable-looking 3x4 patch of tiles that looks like it can't be stillified, but it actually can?

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pcallahan
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Re: Canonical list of still lifes in script-readable form?

Post by pcallahan » July 7th, 2021, 10:36 am

I agree that stabilizing partial patterns makes an interesting puzzle, and it's one I have been doing with my set of physical tiles. It was also the basis for the applet I wrote 25 years ago (that can still be run in appletviewer if you have it, though that even that is missing from my latest Java installation; maybe it's worth promoting this to a standalone app).
dvgrn wrote:
July 7th, 2021, 9:20 am
What's the most improbable-looking 3x4 patch of tiles that looks like it can't be stillified, but it actually can?
I haven't considered enumerating the best examples though. One side question is how to rank the difficulty of any puzzle. When there are very few (or one unique) solution(s) it may be easy to solve if each step is constrained along the way. If there are very many solutions, it's easy to find one by chance. I guess a hard case would involve many choices that work when you place them but send you down blind alleys that can't be completed. It might even be possible to find those by running a backtracking search and collecting metrics on failures.

Finally, while the whole point of these tiles is to have a self-checking system that can be used offline, I wonder if I should invest some time in writing an app.

Added: Another idea for puzzles is to use the tile mulisets with more than one solution instead of avoiding them. For instance, the tiles 14⠁8⠃6⠊2⠋ result in the following 12-cell still lifes.
mult1.png
mult1.png (4.01 MiB) Viewed 797 times
I can't think of a "puzzle" other than keep building till you find all 12 distinct patterns, which is a bit tedious, but maybe there is some idea that works. (There is some room for intuition above. E.g. 4 of these consist of tubs with two tails placed in different ways.)

The number of solutions increases with pattern size. For instance the tiles 16⠁10⠃4⠊4⠋ can be used to make 50 different 14-cell still lifes.

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