LLSSS min height search results

[amling]

... finding spaceships of minimal height.

I can however take a look with what I have for free (my attention and 120GB) and see what I can do.

I'll dump the results and/or any extensive essays about the philosophy of Z^3 geometry here.

I'm going to start with the "staggered" windows. For 1c/N they match the unstaggered windows only they have a possible finer grain measurement.

For c/2 height 7.5 longest partial was:

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| ...***.**... | ...*.****... |
| ...*........ | ..*......... |
| ...******... | ...******... |
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| ...*.*.*.... | ..***..*.... |
| ..**..**.*.. | ..*..*.*.... |
| ...**..*.... |              |

Height 8 finds the known ship.

For c/3 height 4 2/3 longest partial was:

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| ....*.*.. |           |           |

Height 5 finds the known ship.

For c/4 height 7 1/4 the longest partial was:

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| ...*........ | ..**.***.... | ..*....*.... | ..*...**.... |
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| ....*.**.... | .....***.... | ....**.*.... | ...***...... |
| ...*..**.... | ...*...*.... | ..**.*.**... | ..*..*...... |
| ...***...... | ..**.*..*... | ..**..***... | ..**.*..*... |
| ...*...**... | ...*...*.... | .....*...... | ........*... |
| .....**..... | ..***.***... | ..*****.*... | ...****..... |
| ..**.....*.. | ......*..... | ............ | ............ |
| .......*.... | ....**.**... | ....*....... |              |

Height 7.5 finds the ship linked from the wiki (although it says "height 8" there).

For 2c/4 height 4.5 the longest partial was:

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|  ...**.... |  ..***.... | ...*..*..  | ...***...  |
|  ..**..... |  ....**... | ......*..  |            |

Height 5 finds the LWSS.

[amling]

I'll dump ... any extensive essays about the philosophy of Z^3 geometry here.

I guess the shortest version is that I find it undesireable that a c/2 ship, measured as a 2c/4 ship, has a different height when using unstaggered height. With staggered height it has the same height as Nc/2N for any N.

The most concise fully-mathed-up version is that when gcd(n, d) = 1, Z^2/(-n, d) is isomorphic to Z and measuring by the envelope in that Z seems like a more obvious choice. For gcd-with velocities there is still an obvious map from Z^2/(-kn, kd) -> Z^2/(-n, d) =~ Z and still the same obvious choice of measurement. In either case this corresponds to staggered height (rescaled to measure in terms of cells instead of in terms of that generator of Z^2/(-n, d)).

I guess the essay's not as extensive as I thought. Maybe I'll draw some pictures/grids later to try to illustrate what I mean...

[amling]

For c/5 height 7.4 longest partial was:

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| ............ | ....***..... | ....*..*.... | ............ | ............ |
| ...*****.... | ....****.... | ............ | ...**....... | ...**....... |
| ......*.*... | ...**.*.*... | ...**...*... | ...*..**.... | ..**.***.... |
| ..*......*.. | .......*.... | ...*****.... | ...*..**.... | ..**..**.... |
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| ..**.....*.. | ..**........ | ..**........ | ..*.*....... | .....*...... |
| ...*........ | .....*...... | ....*....... | ....*.*..... |              |

Height 7.6 found the spider.

[amling]

2c/5 (staggered) height 9.2 longest partial was:

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|  ......*...*... |  .....***...... |  .....****..... | ......*..*....  | .....******...  |
|  .....*.*...... |  ....*..*.**... |  ....*..**..... | .....*...**...  | ....*...*.....  |
|  ....***..**... |  ....***....... |  ....*.....*... | ....***..**...  | ....*....**...  |
|  .............. |  .....*****.... |  ....*....*.... | .....**.......  | ....*..*......  |
|  .......**..... |  .......**..... |  .....*........ | ......*.......  | ..............  |
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|  .....*.***.*.. |  .......**..... |  .....*..*..... | .....*....*...  | .....**..**...  |
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|  ....*.*.*..*.. |  .....**.*.*... |  ...***.**.*... | ....**..*.*...  | ...***.**.*...  |
|  ...*..****.... |  ..**....***... |  ..*...*...*... | ...*.....**...  | ..*..*....*...  |
|  ..**.**...*... |  ..****..**.... |  ..*..*.*...... | ..***...**....  | ..*.*...*.....  |
|  ......*....... |  ....*..*..*... |  ..*....*.*.... | ...*......*...  | ..*..*....*...  |
|  .....**..*.*.. |  ...**.**...... |  ...*******.... | ....**....*...  | ....**........  |
|  ..***.*....... |  ..*.....*.*... |  ....*.*....... | .....*........  | .....*.****...  |
|  ...**.**.*.... |  ....*.*....... |  ..*....*...... |                 |                 |

2c/5 height 9.4 filled memory (even 120G) and died.

c/6 height 7 1/6 longest partial was:

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| .....*...... | ....*....... | ............ | ....*....... | ............ | ....*....... |
| ...**....... | ....*....... | ...***...... | ....*....... | ...***...... | ...*.*...... |
| ............ | ....*....... | ............ | ...*.*...... | ...*.*...... | ..**........ |
| .....*...... | ............ | ....*....... | ....**...... | ...*.**..... | ..**........ |
| ....*....... | ....***..... | ....**...... | ...*.*...... | ...*.**..... | ...*...*.... |
| ...*.*.*.... | ...*........ | ...*.*...... | ..*..*...... | ..**.**..... | ..*......... |
| ...****..... | ...*........ | ..***....... | ..*..*...... | ...***...... | ..**.**..... |
| ....****.... | ...*...*.... | ....*....... | ....*....... | ............ | ....*....... |
| ........*... | .....*..*... | ........*... | .......*.... | .......*.... | .......*.... |
| .......*.*.. | ......**.... | ......**.... | ......*.*... | ......*.*... | ......*.*... |
| ......**.... | ............ | ......**.... | ......**.... | .....*..*... | ......*.*... |
| ......***... | .....*..*... | ............ | .....*.*.... | .......*.... | ......*..... |
| ......*..... | .....*..*... | .....**..... | ............ | .....*...... | .....*...... |
| .....*.*.... | ....**...... | ............ | .....**..... | .....**..... | .....**..... |
| ....**...... | ....***..... | ...*..*..... | .....*...... | ............ | ....*.*..... |
| ............ | ....**...... | ....*.*..... | ...**.*..... | ...**.*..... | ...**.**.... |
| ....*....*.. | ............ | ....**...... | ....*.*..... | ...**.**.... | ...**.**.... |
| ........*... | .....*...... | .....*...... | .....**..... | ......*..... | .....***.... |
| .....**..... | .....***.... | ....*..*.... | ....**...... | ............ | .....*...... |
| .....**..... | .....**..... | ....*....... | ....***..... | ....*.*..... | .....*...... |
| ............ | .....***.... | .....*.*.... | ......*..... | ......*..... | .....*.*.... |
| ......*.*... | .......*.... | .......*.... | .......**... | ........*... | .......*.... |
| ......*..... | .....**..... | ......**.... | ......**.... | ......*..... | .....**..... |
| ......*.*... | .......*.... | .....*...... | ....*..*.... | .....***.... | .....***.... |
| ............ | .....*...... | ....***..... | ....*....... | ............ | ............ |
| ....**...... | ....**...... | .....**..... | ............ | ...***...... | ...***...... |
| ...*.*...... | ...*.*...... | ...*.*...... | ..**.**..... | ..*..*...... | ..*......... |
| ...*........ | ...*........ | ..**........ | ..***....... | ..*.****.... | ..*....**... |
| ....****.... | ...*...**... | .......**... | .......**... | ...**..**... | ...**....... |
| ....**.**... | ........*... | .......**... | .....*..*... | .......**... | ....*.***... |
| .....*.*.... | .....*...... | ....***..... | ....*....... | .....*...... | ......*..... |
| .....*.**... | ....**.*.... | ...*.**..... | ......*..... | .....*...... | ....**...... |
| ....*..*.*.. | ...**....... | ............ | ....*..*.... | ....*...*... | ....*.*.*... |
| ...**.**.... | ..*.*....... | ....*.**.... | ....*****... | ....*.***... | ....**.**... |
| ..**..**.... | .....****... | ...*.*.**... | ..*.*....... | ..**........ |              |

c/6 height 7 1/3 filled memory and died.

Maybe LLSSS is not a good choice for this with no memory/CPU tradeoff to fall back on. I might try with LGOL although I'm not optimistic and I doubt it's better than whatever Sokwe used in 2015. I also had a crazy idea for a memory/CPU tradeoff for fixed-board LLSSS but it's gonna be extremely slow and a lot of code. TBD.

[Sokwe]

I came back to this topic because I've been expanding the minimum height tables on the spaceship search status page.

I doubt it's better than whatever Sokwe used in 2015.

The c/7 height-8, c/6 height-9, and 2c/5 height-10 searches were actually done in 2010 or 2011 with WLS. In the c/6 and c/7 cases, the search was split up over dozens of computers in a computer lab I had some relatively exclusive access to on weekends (although I'm sure I wasn't supposed to be running Life searches). These took long enough that they might still be hard to replicate even with modern tools and hardware.

The 2c/5 search was done on my personal computer, but it took weeks, or maybe months. I can't remember.

2c/5 height 9.4 filled memory (even 120G) and died...

Maybe LLSSS is not a good choice for this with no memory/CPU tradeoff to fall back on. I might try with LGOL although I'm not optimistic and I doubt it's better than whatever Sokwe used in 2015.

I am wondering if at least the height-10 2c/5 result could still be confirmed with LGOL. Is there any difficulty in this, or would it just take too much time? If it's a matter of the search taking up valuable computer resources, I'd be willing to run it, but I don't know how to set it up, and I've never used LGOL. My goal would primarily be to confirm that there are no (2,0)c/5 ships that fit in a height-10 bounding box through their whole period, but I wouldn't mind knowing the fine-grain staggered minimum as well.

[amling]

Maybe LLSSS is not a good choice for this with no memory/CPU tradeoff to fall back on. I might try with LGOL although I'm not optimistic and I doubt it's better than whatever Sokwe used in 2015.

I am wondering if at least the height-10 2c/5 result could still be confirmed with LGOL. Is there any difficulty in this, or would it just take too much time? If it's a matter of the search taking up valuable computer resources, I'd be willing to run it, but I don't know how to set it up, and I've never used LGOL. My goal would primarily be to confirm that there are no (2,0)c/5 ships that fit in a height-10 bounding box through their whole period, but I wouldn't mind knowing the fine-grain staggered minimum as well.

Sadly LGOL makes LLSSS look user friendly so it's gonna be a bit of a mess. Running staggered heights of an integer number of rows up to 12 requires no real code, just the usual "edit 100% of main_lgol to configure your search". This is pushed up to 20240220-2c5-min-height. Run as `cargo run --release 06` e.g. to run height 6 (staggered envelope though, as should be clear in partials).

I have run this just now and some highlights from the output are:

Code: Select all

20240220 10:50:21 [DEBUG] Checks3: compiling table of 17 bits for bgc = GolBgcWrapper(GolBgc1), idx0 = 0
20240220 10:50:22 [DEBUG] Checks3: compiling table of 17 bits for bgc = GolBgcWrapper(GolBgc1), idx0 = 0
20240220 10:50:23 [DEBUG] Checks3: compiling table of 19 bits for bgc = GolBgcWrapper(GolBgc1), idx0 = 8
20240220 10:50:26 [DEBUG] Checks3: compiling table of 18 bits for bgc = GolBgcWrapper(GolBgc1), idx0 = 8
20240220 10:50:27 [DEBUG] Checks3: compiling table of 17 bits for bgc = GolBgcWrapper(GolBgc1), idx0 = 16
20240220 10:50:28 [DEBUG] Checks3: compiling table of 17 bits for bgc = GolBgcWrapper(GolBgc1), idx0 = 16
20240220 10:50:29 [DEBUG] Checks3: compiling table of 11 bits for bgc = GolBgcWrapper(GolBgc1), idx0 = 16
20240220 10:50:29 [DEBUG] Checks3: compiling table of 16 bits for bgc = GolBgcWrapper(GolBgc1), idx0 = 24
20240220 10:50:30 [DEBUG] Checks3: compiling table of 16 bits for bgc = GolBgcWrapper(GolBgc1), idx0 = 24
20240220 10:50:30 [DEBUG] Checks3: compiling table of 13 bits for bgc = GolBgcWrapper(GolBgc1), idx0 = 24
20240220 10:50:30 [INFO] Checks3: compilation took 8.759647413s

Due to the way LGOL picks bits it's going to require somewhat more expensive precompilation than LLSSS. This precompilation should scale linearly with the height. You can set environment variable LGOL_MAX_TABLE_SIZE to something lower (e.g. 9) if you want it to generate smaller tables (quicker to generate, slower to run).

Code: Select all

20240220 10:50:30 [INFO] q 1 (16 B), kns 2 (80 B), total 96 B
20240220 10:50:30 [INFO] Completed BFS step to depth 1 (LGolDepth { r1ld8: 1 })
20240220 10:50:30 [DEBUG] Firstest:
20240220 10:50:30 [DEBUG] |  ...... |  ...... |  ...... | ......  | ......  |
20240220 10:50:30 [DEBUG] |  ...... |  ...... |  ...... | ......  | ......  |
20240220 10:50:30 [DEBUG] |  ...... |  ..???? |  ?????? | ??????  | ??????  |
20240220 10:50:30 [DEBUG] Random partial:
20240220 10:50:30 [DEBUG] |  ...... |  ...... |  ...... | ......  | ......  |
20240220 10:50:30 [DEBUG] |  ...... |  ...... |  ...... | ......  | ......  |
20240220 10:50:30 [DEBUG] |  *.*..* |  ..???? |  ?????? | ??????  | ??????  |
20240220 10:50:30 [INFO] q 150 (2.34 KB), kns 2 (80 B), total 2.42 KB

LGOL doesn't show any bounding zeros, just the window of actually variable cells. You can see it's shifted in later generations.

Code: Select all

20240220 10:50:31 [INFO] q 48276096 (736.63 MB), kns 2 (80 B), total 736.63 MB
20240220 10:50:32 [INFO] par: threads 8/8, completed 179/737
20240220 10:50:34 [INFO] par: threads 8/8, completed 597/737
20240220 10:50:42 [INFO] Completed BFS step to depth 5 (LGolDepth { r1ld8: 0 })

It will output these "par:" lines if a step is taking sufficiently long to try to give some idea of what's happening and/or evidence it is still running.

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20240220 10:50:42 [INFO] End "" -> ():
20240220 10:50:42 [INFO] |  ...... |  ...... |  ...... | ......  | ......  |
20240220 10:50:42 [INFO] |  ...... |  ...... |  ...... | ......  | ......  |
20240220 10:50:42 [INFO] |  ...... |  ...... |  ...... | ......  | ......  |

"End" means (as I've configured it) that it got back to all zeros. This one is the trivial one, but if there were any ships you'd get more.

Code: Select all

20240220 10:50:59 [INFO] q 85065276 (1.27 GB), kns 48276097 (1.80 GB), total 3.07 GB
20240220 10:51:01 [INFO] par: threads 8/8, completed 123/800
20240220 10:51:03 [INFO] par: threads 8/8, completed 375/800
20240220 10:51:06 [INFO] ws.q 6241056 (95.23 MB), ws.q2 78824220 (4.11 GB), kns 48276097 (1.80 GB), total 6.00 GB, deepening...
20240220 10:51:06 [INFO] Deepened ws.q 6241056 => 6241056, foresight 1 in 42.881109ms
20240220 10:51:07 [INFO] Deepened ws.q2 78824220 => 78824220, foresight 0 in 380.58697ms
20240220 10:51:08 [INFO] Rebuilt kns from 48276097 to 113464 (1 roots) in 903.147573ms
20240220 10:51:08 [INFO] Deepening pass 6.00 GB => 4.21 GB completed in 1.328057661s
20240220 10:51:11 [INFO] Completed BFS step to depth 10 (LGolDepth { r1ld8: 0 })

As LGOL continues on it stores a big tree of partials ("kns" is what it's named above), only appending until it fills memory. By default the code will assume 2 GB, but you can set, as I have here, e.g. BFS_MEM_GB=6 for 6 GB. Note that this is its internal estimate of memory which is inaccurate to say the least. You may want to experiment with values to see what's right for your computer. When the tree reaches the limit, as it did here, it stops and prunes the queue/tree, possibly doing additional filtering via DFS on each node. "Foresight" represents more or less the depths it is searching to to. Values 1 and 0, as seen here, really mean it's just cleaning up unused tree bits. You will certainly see occasional foresight 1/0 passes as it cleans up after itself every time it fills memory, but...

You may also see repeated passes with increasing foresight. This is what happens when your search really exceeds your memory and LGOL is using its nearly limitless capacity to trade off time/memory. I say nearly limitless, but in reality we are only willing to wait for so long and the deeper the DFSing gets the slower it gets, quite badly. Unfortunately it's very hard to tell how long searches are going too take from any of this. Usually I run a sequence of smaller widths up to whatever I'm actually hoping to run to try to get some extrapolated sense.

Code: Select all

20240220 10:51:33 [INFO] Completed BFS step to depth 56 (LGolDepth { r1ld8: 1 })
20240220 10:51:33 [DEBUG] Firstest:
20240220 10:51:33 [DEBUG] |  ...... |  ...... |  ...... | ......  | ......  |
20240220 10:51:33 [DEBUG] |  ...... |  ...... |  ...... | ......  | ......  |
20240220 10:51:33 [DEBUG] |  ...... |  ....*. |  ...**. | ....**  | ....*.  |
20240220 10:51:33 [DEBUG] |  ...*** |  ...**. |  ..*..* | ...*..  | ...*..  |
20240220 10:51:33 [DEBUG] |  ...*.. |  ..**.* |  ..**.. | ...*..  | ..**..  |
20240220 10:51:33 [DEBUG] |  ...*.* |  ...... |  ...**. | ...***  | ...**.  |
20240220 10:51:33 [DEBUG] |  .....* |  ....*. |  ...... | ......  | ....*.  |
20240220 10:51:33 [DEBUG] |  ...... |  ...... |  ...... | ......  | ...*..  |
20240220 10:51:33 [DEBUG] |  ..*..* |  .**... |  .**... | ..***.  | .****.  |
20240220 10:51:33 [DEBUG] |  .**..* |  .*...* |  .*.**. | .**..*  | .*..*.  |
20240220 10:51:33 [DEBUG] |  .*.**. |  ...**. |  *..**. | .*....  | *.....  |
20240220 10:51:33 [DEBUG] |  **.... |  ***... |  .***.. | .**...  | *.**..  |
20240220 10:51:33 [DEBUG] |  ...... |  ...... |  .*..*. | *.*.*.  | *.....  |
20240220 10:51:33 [DEBUG] |  ...... |  ..???? |  ?????? | ??????  | ??????  |
20240220 10:51:33 [DEBUG] Random partial:
20240220 10:51:33 [DEBUG] |  ...... |  ...... |  ...... | ......  | ......  |
20240220 10:51:33 [DEBUG] |  ...... |  ...... |  ...... | ......  | ......  |
20240220 10:51:33 [DEBUG] |  ...... |  ....*. |  ...**. | ....**  | ....*.  |
20240220 10:51:33 [DEBUG] |  ...*** |  ...**. |  ..*..* | ...*..  | ...*..  |
20240220 10:51:33 [DEBUG] |  ...*.. |  ..**.* |  ..**.. | ...*..  | ..**..  |
20240220 10:51:33 [DEBUG] |  ...*.* |  ...... |  ...**. | ...***  | ...**.  |
20240220 10:51:33 [DEBUG] |  .....* |  ....*. |  ...... | ......  | ....*.  |
20240220 10:51:33 [DEBUG] |  ...... |  ...... |  ...... | ......  | ...*..  |
20240220 10:51:33 [DEBUG] |  ..*..* |  .**... |  .**... | ..***.  | .****.  |
20240220 10:51:33 [DEBUG] |  .**..* |  .*...* |  .*.**. | .**..*  | .*..*.  |
20240220 10:51:33 [DEBUG] |  .*.**. |  ...**. |  *..**. | .*....  | *.....  |
20240220 10:51:33 [DEBUG] |  **.... |  ***... |  .***.. | .**...  | *.**..  |
20240220 10:51:33 [DEBUG] |  ...... |  ...... |  *..*.. | *.*.*.  | *....*  |
20240220 10:51:33 [DEBUG] |  ...*.* |  .*???? |  ?????? | ??????  | ??????  |
20240220 10:51:33 [INFO] q 778 (12.16 KB), kns 134922125 (5.03 GB), total 5.03 GB
20240220 10:51:33 [INFO] Completed BFS step to depth 57 (LGolDepth { r1ld8: 2 })
20240220 10:51:33 [INFO] Dumping 0 final partials at lookback 0...
20240220 10:51:33 [INFO] Dumped 0 final partials at lookback 0.
20240220 10:51:33 [INFO] bfs/ex1/bfs_expand/expand loop/expand: 46 calls, 27.907697394s own time, 27.907697394s total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/expand: 12 calls, 12.046897717s own time, 12.046897717s total time
20240220 10:51:33 [INFO] bfs/ex2/q4 foldover: 11 calls, 10.873720048s own time, 10.873720048s total time
20240220 10:51:33 [INFO] bfs/ex1/bfs_expand/rebalance: 46 calls, 7.274370114s own time, 7.274370114s total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/rebalance: 11 calls, 1.800962219s own time, 1.800962219s total time
20240220 10:51:33 [INFO] bfs/ex1/bfs_expand: 46 calls, 1.300115889s own time, 36.512236319s total time
20240220 10:51:33 [INFO] bfs/ex2/q3 reverse: 11 calls, 577.881637ms own time, 577.881637ms total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/deepen q2/deepen: 1 calls, 380.578167ms own time, 380.578167ms total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand: 11 calls, 260.552984ms own time, 15.443650549s total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/rebuild kns/reindex pins: 1 calls, 247.861265ms own time, 247.861265ms total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/rebuild kns/compact: 1 calls, 181.071725ms own time, 181.071725ms total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/rebuild kns/walk pins: 1 calls, 169.821379ms own time, 169.821379ms total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/rebuild kns/compute new positions: 1 calls, 144.039084ms own time, 144.039084ms total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/rebuild kns/reindex self: 1 calls, 116.746236ms own time, 116.746236ms total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/rebuild kns: 1 calls, 44.952272ms own time, 904.49233ms total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/deepen q/deepen: 1 calls, 42.871428ms own time, 42.871428ms total time
20240220 10:51:33 [INFO] bfs/ex1/bfs_expand/q3 foldover: 46 calls, 29.777693ms own time, 29.777693ms total time
20240220 10:51:33 [INFO] bfs/partials: 57 calls, 16.468441ms own time, 16.468441ms total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/q3 foldover: 11 calls, 7.013135ms own time, 7.013135ms total time
20240220 10:51:33 [INFO] bfs: 1 calls, 2.650084ms own time, 63.42672372s total time
20240220 10:51:33 [INFO] bfs/ex1/bfs_expand/expand loop: 46 calls, 275.229µs own time, 27.907972623s total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop: 11 calls, 186.419µs own time, 13.375122211s total time
20240220 10:51:33 [INFO] bfs/ex2: 11 calls, 76.187µs own time, 26.895328421s total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/deepen q2: 1 calls, 49.218µs own time, 380.627385ms total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/deepen q: 1 calls, 46.932µs own time, 42.91836ms total time
20240220 10:51:33 [INFO] bfs/ex1: 46 calls, 35.807µs own time, 36.512272126s total time
20240220 10:51:33 [INFO] bfs/partials tree: 58 calls, 4.648µs own time, 4.648µs total time
20240220 10:51:33 [INFO] bfs/ex2/bfs_expand/expand loop/rebuild kns/compact roots: 1 calls, 369ns own time, 369ns total time
20240220 10:51:33 [INFO] bfs took 63.426928771s
20240220 10:51:34 [INFO] Done

Eventually it finished.

As an example from the next height up, here is it thrashing against the memory limit until it eventually DFSes deep enough to choke through:

Code: Select all

20240220 10:56:43 [INFO] Completed BFS step to depth 9 (LGolDepth { r1ld8: 3 })
20240220 10:56:43 [DEBUG] Firstest:
20240220 10:56:43 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 10:56:43 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 10:56:43 [DEBUG] |  ....... |  ....... |  ....... | .......  | .....*.  |
20240220 10:56:43 [DEBUG] |  ....... |  ....... |  ....... | ...????  | ???????  |
20240220 10:56:43 [DEBUG] Random partial:
20240220 10:56:43 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 10:56:43 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 10:56:43 [DEBUG] |  ..*.*.* |  ...*..* |  ...*.*. | ...*.*.  | ..*..**  |
20240220 10:56:43 [DEBUG] |  ..*..** |  .*****. |  .*.*..* | ..*????  | ???????  |
20240220 10:56:43 [INFO] q 283558052 (4.23 GB), kns 2254557 (86.00 MB), total 4.31 GB
20240220 10:56:47 [INFO] par: threads 8/8, completed 16/800
20240220 10:56:48 [INFO] ws.q 271942406 (4.05 GB), ws.q2 125376773 (1.87 GB), kns 2254557 (86.00 MB), total 6.00 GB, deepening...
20240220 10:56:49 [INFO] par: threads 8/8, completed 132/800
20240220 10:56:51 [INFO] par: threads 8/8, completed 279/800
20240220 10:56:55 [INFO] par: threads 8/8, completed 616/800
20240220 10:56:57 [INFO] Deepened ws.q 271942406 => 119410804, foresight 2 in 9.137599005s
20240220 10:56:58 [INFO] par: threads 8/8, completed 21/800
20240220 10:56:59 [INFO] Deepened ws.q2 125376773 => 99889783, foresight 1 in 1.280879899s
20240220 10:56:59 [INFO] Rebuilt kns from 2254557 to 1313478 (1 roots) in 504.864938ms
20240220 10:56:59 [INFO] Deepening pass 6.00 GB => 3.32 GB completed in 10.923722123s
20240220 10:57:00 [INFO] par: threads 8/8, completed 46/800
20240220 10:57:02 [INFO] ws.q 109709563 (1.63 GB), ws.q2 290024850 (4.32 GB), kns 1313478 (50.11 MB), total 6.01 GB, deepening...
20240220 10:57:03 [INFO] par: threads 8/8, completed 206/800
20240220 10:57:05 [INFO] par: threads 8/8, completed 533/800
20240220 10:57:07 [INFO] Deepened ws.q 109709563 => 109709563, foresight 3 in 4.569973039s
20240220 10:57:08 [INFO] par: threads 8/8, completed 20/800
20240220 10:57:10 [INFO] par: threads 8/8, completed 61/800
20240220 10:57:10 [INFO] Deepened ws.q2 290024850 => 257644432, foresight 2 in 3.307265308s
20240220 10:57:11 [INFO] Rebuilt kns from 1313478 to 1313478 (1 roots) in 799.642034ms
20240220 10:57:11 [INFO] Deepening pass 6.01 GB => 5.52 GB completed in 8.677362606s
20240220 10:57:11 [INFO] ws.q 108617316 (1.62 GB), ws.q2 291052226 (4.34 GB), kns 1313478 (50.11 MB), total 6.00 GB, deepening...
20240220 10:57:12 [INFO] par: threads 8/8, completed 95/800
20240220 10:57:14 [INFO] par: threads 8/8, completed 141/800
20240220 10:57:18 [INFO] par: threads 8/8, completed 324/800
20240220 10:57:25 [INFO] Deepened ws.q 108617316 => 50094743, foresight 4 in 13.666118979s
20240220 10:57:26 [INFO] par: threads 8/8, completed 8/800
20240220 10:57:28 [INFO] par: threads 8/8, completed 23/800
20240220 10:57:32 [INFO] par: threads 8/8, completed 53/800
20240220 10:57:33 [INFO] Deepened ws.q2 291052226 => 127615515, foresight 3 in 8.371579712s
20240220 10:57:34 [INFO] Rebuilt kns from 1313478 to 788948 (1 roots) in 458.28309ms
20240220 10:57:34 [INFO] Deepening pass 6.00 GB => 2.68 GB completed in 22.496539549s
20240220 10:57:35 [INFO] par: threads 8/8, completed 96/800
20240220 10:57:37 [INFO] par: threads 8/8, completed 164/800
20240220 10:57:38 [INFO] ws.q 37157625 (566.98 MB), ws.q2 363758054 (5.42 GB), kns 788948 (30.10 MB), total 6.00 GB, deepening...
20240220 10:57:39 [INFO] par: threads 8/8, completed 272/800
20240220 10:57:41 [INFO] par: threads 8/8, completed 321/800
20240220 10:57:45 [INFO] par: threads 8/8, completed 484/800
20240220 10:57:53 [INFO] par: threads 8/8, completed 704/800
20240220 10:57:56 [INFO] Deepened ws.q 37157625 => 4799068, foresight 5 in 18.082256259s
20240220 10:57:57 [INFO] par: threads 8/8, completed 0/800
20240220 10:57:59 [INFO] par: threads 8/8, completed 14/800
20240220 10:58:03 [INFO] par: threads 8/8, completed 23/800
20240220 10:58:11 [INFO] par: threads 8/8, completed 46/800
20240220 10:58:25 [INFO] Deepened ws.q2 363758054 => 40221562, foresight 4 in 28.851239426s
20240220 10:58:25 [INFO] Rebuilt kns from 788948 to 211733 (1 roots) in 100.597466ms
20240220 10:58:25 [INFO] Deepening pass 6.00 GB => 695.04 MB completed in 47.034439556s
20240220 10:58:26 [INFO] Completed BFS step to depth 10 (LGolDepth { r1ld8: 4 })
20240220 10:58:26 [DEBUG] Firstest:
20240220 10:58:26 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 10:58:26 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 10:58:26 [DEBUG] |  ....... |  ....... |  ....... | .......  | .....*.  |
20240220 10:58:26 [DEBUG] |  ....... |  ....... |  ....... | ....***  | ....???  |
20240220 10:58:26 [DEBUG] Random partial:
20240220 10:58:26 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 10:58:26 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 10:58:26 [DEBUG] |  ...*.** |  ....... |  ....... | ..*....  | ..*....  |
20240220 10:58:26 [DEBUG] |  .*..... |  .*.*..* |  ***.*.* | .*.*.**  | .*.*???  |
20240220 10:58:26 [INFO] q 60135757 (917.60 MB), kns 211733 (8.08 MB), total 925.68 MB

Please give the pushed branch a spin. As-is it's only staggered envelopes but I believe it should be enough to get a sense of whether or not LGOL has any shot of completing what you want. If you decide you like what you see, just let me know and I will dig into implementing some hacks to limit some cells to zero and thereby allow unstaggered envelope searches.

EDIT:

I sketched a pretty sloppy version of unstaggered windows (pushed as 20240220-2c5-min-height-unstaggered). It integrates as what LGOL calls a "constraint" which is maybe mid-way through the process. Earlier would likely perform better but to do any earlier involves wading into super complex table precompilation code which I would really rather not do. Later (as some sort of post-expansion filter) would not really be any easier and would likely perform materially worse anyway.

Due to being somewhat generic the numbers are maybe off by one from what you'd expect. It runs a normal LGOL search which is staggered but then restricts all generations to have the intersection of their X coordinate windows. So e.g. If you run `cargo run --release 07` it shows this:

Code: Select all

20240220 12:10:32 [INFO] Stagger constraint:
20240220 12:10:32 [INFO] |  ??????. |  ??????. |  ??????. | .??????  | .??????  |

You can see each generation is still 7 wide but it's indicating it's going to force one cell on one edge or the other off when it gets there, making this unstaggered height 6. This is sufficiently generic that it should work for any wacky choice of s2s geometry, but that delta between staggered and unstaggered may vary. You can always read this "Stagger constraint:" printout to see what it is going to do.

That same search (`cargo run --release 07`) goes on to print as final partials:

Code: Select all

20240220 12:11:37 [INFO] Completed BFS step to depth 63 (LGolDepth { r1ld8: 3 })
20240220 12:11:37 [DEBUG] Firstest:
20240220 12:11:37 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 12:11:37 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 12:11:37 [DEBUG] |  ....... |  ....*.. |  ...**.. | ....**.  | ....*..  |
20240220 12:11:37 [DEBUG] |  ...***. |  ...**.. |  ...**.. | ...*...  | ...*...  |
20240220 12:11:37 [DEBUG] |  ...*... |  ...*... |  ...*... | ...*...  | ..**...  |
20240220 12:11:37 [DEBUG] |  ....... |  ....*.. |  ...**.. | ...**..  | ...**..  |
20240220 12:11:37 [DEBUG] |  ....**. |  ...*.*. |  ...*.*. | .......  | ...**..  |
20240220 12:11:37 [DEBUG] |  ...***. |  ...*.*. |  ..**... | ...*...  | .......  |
20240220 12:11:37 [DEBUG] |  ....... |  ..*.... |  ..*.*.. | ..*..*.  | .**..*.  |
20240220 12:11:37 [DEBUG] |  ..**... |  ..**... |  .*.*... | .**.**.  | ......*  |
20240220 12:11:37 [DEBUG] |  ...*... |  .*.*... |  **.*... | .**.**.  | .*.....  |
20240220 12:11:37 [DEBUG] |  .**.... |  **..... |  ....*.. | ...****  | ..**...  |
20240220 12:11:37 [DEBUG] |  **.***. |  **..**. |  **..**. | ...????  | ???????  |
20240220 12:11:37 [DEBUG] Random partial:
20240220 12:11:37 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 12:11:37 [DEBUG] |  ....... |  ....... |  ....... | .......  | .......  |
20240220 12:11:37 [DEBUG] |  .....*. |  ....... |  ....*.. | ....**.  | ....**.  |
20240220 12:11:37 [DEBUG] |  ....*.. |  ...***. |  ...**.. | ...*..*  | ...*...  |
20240220 12:11:37 [DEBUG] |  ...**.. |  ...*... |  ..**.*. | ...**..  | ...*...  |
20240220 12:11:37 [DEBUG] |  ....**. |  ...*.*. |  ....... | ....**.  | ...***.  |
20240220 12:11:37 [DEBUG] |  .....*. |  .....*. |  ....*.. | .......  | .......  |
20240220 12:11:37 [DEBUG] |  ....*.. |  ....... |  ....... | .......  | .......  |
20240220 12:11:37 [DEBUG] |  ..****. |  ..*..*. |  .**.... | ..**...  | ..***..  |
20240220 12:11:37 [DEBUG] |  ..*..*. |  .**..*. |  .*...*. | ..*.**.  | .**..*.  |
20240220 12:11:37 [DEBUG] |  .*..... |  .*.**.. |  ...**.. | .*..**.  | .*.....  |
20240220 12:11:37 [DEBUG] |  .***.*. |  ***.... |  ****... | ..***..  | .**....  |
20240220 12:11:37 [DEBUG] |  *...... |  ....... |  .....*. | .*.????  | ???????  |
20240220 12:11:37 [INFO] q 184 (2.88 KB), kns 112316241 (4.18 GB), total 4.18 GB

Which is at least a little evidence it's working as expected. I'll leave it to you to experiment and see if anything is within range for your computing and time resources.

[Sokwe]

Thanks! I'll work off of 20240220-2c5-min-height-unstaggered for now, which compiled and ran fine. I have a few very simple questions that you shouldn't bother going into too much detail in answering.

By default the code will assume 2 GB, but you can set, as I have here, e.g. BFS_MEM_GB=6 for 6 GB. Note that this is its internal estimate of memory which is inaccurate to say the least. You may want to experiment with values to see what's right for your computer.

Is there any reason not to give the breadth first search as much memory as I have available? That is, could it run slower with a higher memory setting? (for an example of how this could happen, to simplify qfind, I only used multithreading during the depth first lookahead, so setting the BFS memory too large means qfind never enters the depth first search and so doesn't take advantage of multithreading).

Due to the way LGOL picks bits it's going to require somewhat more expensive precompilation than LLSSS. This precompilation should scale linearly with the height. You can set environment variable LGOL_MAX_TABLE_SIZE to something lower (e.g. 9) if you want it to generate smaller tables (quicker to generate, slower to run).

Just to be clear, the "precompilation" refers to runtime-calculated tables, rather than compiled code, right? Or do I have to change the code and recompile for different heights?

Due to being somewhat generic the numbers are maybe off by one from what you'd expect.

Does this mean I need to run `cargo run --release 11` to eliminate height 10?

[amling]

Is there any reason not to give the breadth first search as much memory as I have available? That is, could it run slower with a higher memory setting? (for an example of how this could happen, to simplify qfind, I only used multithreading during the depth first lookahead, so setting the BFS memory too large means qfind never enters the depth first search and so doesn't take advantage of multithreading).

The short answer is I would give it all the memory you got. I can think of at least a few ways it could be slower, but I think on the whole bigger is better and I have always run all my searches on computers where I have ~60 GB with "48 GB" limits.

One way is smaller working set is better and for searches that are not at their worst bottleneck most of memory is full of useless tree that could be cleaned up, but we don't garbage collect these things until we hit the memory ceiling.

Another is that less memory means more DFS pruning and the DFS pruning's handling of cycles is different and while in some ways it's worse, in some ways it could be better. The main BFS search's check for cycles is an expensive hash lookup in a hash we maintain of the path of nodes we're currently expanding while for the DFS pruning search we just don't worry about it and let cycles be found repeatedly until they hit the depth limit and fail the prune.

Due to the way LGOL picks bits it's going to require somewhat more expensive precompilation than LLSSS.

Just to be clear, the "precompilation" refers to runtime-calculated tables, rather than compiled code, right? Or do I have to change the code and recompile for different heights?

Yeah, it's all runtime "precompilation" of the tables that drive the CA checks. I just mean to say don't be alarmed if it takes a long time to start up before it starts outputting the first partials. If you find that table computation too slow you can tune it.

Due to being somewhat generic the numbers are maybe off by one from what you'd expect.

Does this mean I need to run `cargo run --release 11` to eliminate height 10?

Yeah, with that it should output that "Stagger constraint:" display with ten question marks in each generation.

[Sokwe]

The main BFS search's check for cycles is an expensive hash lookup in a hash we maintain of the path of nodes we're currently expanding while for the DFS pruning search we just don't worry about it and let cycles be found repeatedly until they hit the depth limit and fail the prune.

This cycle elimination makes me wonder, could LGOL potentially be used with little to no modification to eliminate the possibility of an unstaggered height-8 (2,0)c/6 ship? There is a known height-9 ship, and at height 7, a 2c/6 search with Nicolay's WLS 6.3 returns 5 ships, all with period 3. However, at height 8 there are infinitely many p3 ships, and WLS 6.3 has no cycle elimination, so it can't rule out the possibility of a p6 ship.

I would consider this 2c/6 search more important than reaffirming old results.

[amling]

The main BFS search's check for cycles is an expensive hash lookup in a hash we maintain of the path of nodes we're currently expanding while for the DFS pruning search we just don't worry about it and let cycles be found repeatedly until they hit the depth limit and fail the prune.

This cycle elimination makes me wonder, could LGOL potentially be used with little to no modification to eliminate the possibility of an unstaggered height-8 (2,0)c/6 ship? There is a known height-9 ship, and at height 7, a 2c/6 search with Nicolay's WLS 6.3 returns 5 ships, all with period 3. However, at height 8 there are infinitely many p3 ships, and WLS 6.3 has no cycle elimination, so it can't rule out the possibility of a p6 ship.

I would consider this 2c/6 search more important than reaffirming old results.

"Could" and "are you gonna like it" are not always the same question... you can definitely run that search and in a theoretical sense it should be finite and terminate[able]. The problems are (a) it may take a very, very long time, and (b) its notion of separation is only the strongest, namely two full rows of zeros, and so it's going to output possibly quite a fountain of useless combinations of the known ships barely brushing up against each other.

If you change "(-2, 0, 5)" to "(-2, 0, 6)" in src/entry.rs on the 2c/5 unstaggered branch it should be ready to go to do this search (for 2c/6 the unstaggered envelope size and program argument will be off by one so `cargo run --release 09` for 8 unstaggered height). I would advise running smaller heights first to see how long they take and to see how you feel about the uselessly duplicated output.

EDIT:

I completed unstaggered height 6 just to test this and it took about an hour on my very highly-loaded laptop with `BFS_MEM_GB=6`. Even from just the one ship it finds 11 "ends" or "cycles" that to human eyes are clearly recombinations of the one ship, but in LGOL's technical sense are all valid/distinct paths/cycles in the graph of 2-row states. As an example the longest partial was this:

Code: Select all

|  ....... |  ....... |  ....... | .......  | .......  | .......  |
|  ....... |  ....... |  ....... | .......  | .......  | .......  |
|  .....*. |  ....*.. |  ....*.. | .....*.  | ....*..  | ....*..  |
|  ...**.. |  ...*.*. |  ...*.*. | ...**..  | ...*.*.  | ...*.*.  |
|  ...**.. |  ...*.*. |  ..**... | ...**..  | ...*.*.  | ..**...  |
|  .....*. |  ...*... |  ...*... | .....*.  | ...*...  | ...*...  |
|  ...*... |  ..**... |  ..*.*.. | ...*...  | ..**...  | ..*.*..  |
|  ..***.. |  ..*.*.. |  ..*.... | ..***..  | ..*.*..  | ..*....  |
|  ..*.... |  ....... |  .*..... | ..*....  | .......  | .*.....  |
|  .**.... |  .***... |  .*.*... | .**....  | .***...  | .*.*...  |
|  ...*... |  .*.*... |  .*..*.. | ...*...  | .*.*...  | .*..*..  |
|  ..*.*.. |  ..*.*.. |  ....... | ..*.*..  | ..*.*..  | .......  |
|  ..*.*.. |  .**.... |  .***... | ..*.*..  | .**....  | .***...  |
|  ..*.... |  ....... |  .**.... | ..*....  | .......  | .**....  |
|  ....*.. |  ..*.... |  ...*... | ....*..  | ..*....  | ...*...  |
|  ..**... |  ..*.*.. |  .**.... | ..**...  | ..*.*..  | .**....  |
|  ..**... |  ..*.*.. |  ..*.*.. | ..**...  | ..*.*..  | ..*.*..  |
|  ....*.. |  ...*... |  ...*... | ....*..  | ...*...  | ...*...  |
|  ....... |  ....... |  ....... | .......  | .......  | .......  |
|  ....*.. |  ...*... |  ...*... | ....*..  | ...*...  | ...*...  |
|  ..**... |  ..*.*.. |  ..*.*.. | ..**...  | ..*.*..  | ..*.*..  |
|  ..**... |  ..*.*.. |  .**.... | ..**...  | ..*.*..  | .**....  |
|  ....*.. |  ..*.... |  ...*... | ....*..  | ..*....  | ...*...  |
|  ..*.... |  ....... |  .**.... | ..*....  | .......  | .**....  |
|  ..*.*.. |  .**.... |  .***... | ..*.*..  | .**....  | .***...  |
|  ..*.*.. |  ..*.*.. |  ....... | ..*.*..  | ..*.*..  | .......  |
|  ...*... |  .*.*... |  .*..*.. | ...*...  | .*.*...  | .*..*..  |
|  .**.... |  .***... |  .*.*... | .**....  | .***...  | .*.*...  |
|  ..*.... |  ....... |  .*..... | ..*....  | .......  | .*.....  |
|  ..***.. |  ..*.*.. |  ..*.... | ..***..  | ..*.*..  | ..*....  |
|  ...*... |  ..**... |  ..*.*.. | ...*...  | ..**...  | ..*.*..  |
|  .....*. |  ...*... |  ...*... | .....*.  | ...*...  | ...*...  |
|  ...**.. |  ...*.*. |  ..**... | ...**..  | ...*.*.  | ..**...  |
|  ...**.. |  ...*.*. |  ...*.*. | ...**..  | ...*.*.  | ...*.*.  |
|  .....*. |  ....*.. |  ....*.. | .....*.  | ....*..  | ....*..  |
|  ....... |  ....... |  ....... | .......  | .......  | .......  |
|  ....*.. |  ....*.. |  ...*... | ....*..  | ....*..  | ...*...  |
|  ...*.*. |  ..**... |  ..*.*.. | ...*.*.  | ..**...  | ..*.*..  |
|  ..**... |  ..**... |  ..*.*.. | ..**...  | ..**...  | ..*.*..  |
|  ....*.. |  ....*.. |  ..*.... | ....*..  | ....*..  | ..*....  |
|  ..**... |  ..*.... |  ....... | ..**...  | ..*....  | .......  |
|  ..***.. |  ..*.*.. |  .**.... | ..***..  | ..*.*..  | .**....  |
|  ....... |  ..*.*.. |  ..*.*.. | .......  | ..*.*..  | ..*.*..  |
|  ..*..*. |  ...*... |  .*.*... | ..*..*.  | ...*...  | .*.*...  |
|  ..*.*.. |  .**.... |  .***... | ..*.*..  | .**....  | .***...  |
|  ..*.... |  ..*.... |  ....... | ..*....  | ..*....  | .......  |
|  ...*... |  ..***.. |  ..*.*.. | ...*...  | ..***..  | ..*.*..  |
|  ...*.*. |  ...*... |  ..**... | ...*.*.  | ...*...  | ..**...  |
|  ....*.. |  .....*. |  ...*... | ....*..  | .....*.  | ...*...  |
|  ...**.. |  ...**.. |  ...*.*. | ...**..  | ...**..  | ...*.*.  |
|  ....... |  ...**.. |  ...**.. | .......  | ...**..  | ...**..  |
|  ..*..*. |  ....... |  ..**... | ..*..*.  | .......  | ..**...  |
|  ..*.... |  .**.... |  .**.... | ..*....  | .**....  | .**....  |
|  ..**... |  ..***.. |  .*..*.. | ..**...  | ..***..  | .*..*..  |
|  ...*.*. |  ...*... |  ....... | ...*.*.  | ...*...  | .......  |
|  ...*.*. |  ..**... |  ..***.. | ...*.*.  | ..**...  | ..***..  |
|  ...*... |  ...*... |  ..**... | ...*...  | ...*...  | ..**...  |
|  ....*.. |  ....... |  ....*.. | ....*..  | .......  | ....*..  |
|  ....... |  ...*.*. |  ....... | .......  | ....**.  | .......  |
|  ...***. |  ...*.*. |  ...*... | ....**.  | .......  | ..*..*.  |
|  ..*.**. |  .**.... |  .***.*. | .**....  | .****..  | .*.**..  |
|  .**.*.. |  .*..**. |  **.**.. | .*..*.*  | .*.*.*.  | .*.....  |
|  ..**... |  *..*... |  .*...*. | ..*...*  | ...*...  | .*.*.*.  |
|  **..... |  ..***.. |  .*...*. | ....*..  | .**.???  | ???????  |

Technically each slice of 2 rows is unique and nonzero, but it's obviously silly. I assume by width 8 it's going to be an avalanche of this crud. If you do go on to run width 8 and you want to figure out "was there any non-c/3 stuff in this log file", that is probably something a little shell scripting and `grid-tool pd-fold 2c6-s2s 2` can do the hard work on. I guess let me know when/if you go there.

[Sokwe]

it's going to output possibly quite a fountain of useless combinations of the known ships barely brushing up against each other....

As an example the longest partial was this:

Code: Select all

...

Technically each slice of 2 rows is unique and nonzero

Does it only check if the current partial result has a cycle, and not whether the latest 2-row block added was already seen in the overall graph of all partial results? It would seem that graph-wide duplicate row elimination would prevent it from finding two ships right next to each other. Of course, it would need to not drop any unique part of the graph in the current partial result that precedes the duplicate rows.

qfind gives an example of how not to do things. I think I've explained this before, but if qfind sees a new 2-full-rows chunk that's already in the graph, it discards that branch. Unfortunately, even though that branch was currently at a previously seen state, some earlier part of the branch might not have occurred in any other part of the graph. Thus qfind basically can't find pushalongs, as their back end is a spaceship that would have already showed up earlier in the search.

I don't really know how LGOL works, so I don't know if this could be reasonably or even possibly implemented. It's very low priority, anyway. The discussion you're having with David Bell is much more important. I could probably write a qfind-like search that could accomplish my goal in this case. I might do that if nobody else finds a way to eliminate 2c/6 height-8 anytime soon.

[amling]

it's going to output possibly quite a fountain of useless combinations of the known ships barely brushing up against each other....

As an example the longest partial was this:

Code: Select all

...

Technically each slice of 2 rows is unique and nonzero

Does it only check if the current partial result has a cycle, and not whether the latest 2-row block added was already seen in the overall graph of all partial results? It would seem that graph-wide duplicate row elimination would prevent it from finding two ships right next to each other. Of course, it would need to not drop any unique part of the graph in the current partial result that precedes the duplicate rows.

qfind gives an example of how not to do things. I think I've explained this before, but if qfind sees a new 2-full-rows chunk that's already in the graph, it discards that branch. Unfortunately, even though that branch was currently at a previously seen state, some earlier part of the branch might not have occurred in any other part of the graph. Thus qfind basically can't find pushalongs, as their back end is a spaceship that would have already showed up earlier in the search.

I don't really know how LGOL works, so I don't know if this could be reasonably or even possibly implemented. It's very low priority, anyway. The discussion you're having with David Bell is much more important. I could probably write a qfind-like search that could accomplish my goal in this case. I might do that if nobody else finds a way to eliminate 2c/6 height-8 anytime soon.

What LGOL has, or is possibly close to having:

What LGOL calls "cycle" detection only finds 2 row slices that are a parent in the tree and thus form, well, a cycle. I have never wanted to not detect and prune these (as they're guaranteed to be repeatable forever) although I have occasionally deleted the printing out of them for searches where they are numerous and not helpful.

LGOL has a feature called "deduplication" where it will track globally and forever certain slices it has seen and refuse to enter them (a second time). By default this is off, or rather is enabled for no slices. I have occasionally used it configured with all slices but this tends to balloon up and occupy a lot of memory that it will never release. More often I have used it with some subset of slices big enough to split the graph up somewhat, but small enough to not take up too much memory. As an example, I have certainly had it save all reduced period slices, and that is something we might try here (saving all strict c/3 slices in this 2c/6 search). This feature (in any form) is not something I remember using a lot and the only win for it I can remember offhand is the search for the zebra stripes space clearer 5c/5 corner.

I have had at one time or another a fairly hacked-up branch where it would refuse to enter a slice that was present elsewhere in the tree still in consideration (which I seem to recall being told is what e.g. gfind does), but this has never been cleaned up and shipped in any form. I don't even recall if I ever used it in a successful search for anything.

[amling]

I am wondering if at least the height-10 2c/5 result could still be confirmed with LGOL.

I was able to confirm this (no height 10 unstaggered 2c/5 ships) with LLSSS. No doubt not the most efficient way as it took ~11h and reached ~270 GB of memory. Last partial output was:

Code: Select all

x = 96, y = 103, rule = LifeHistory
F2.15B.F2.15B.F2.15B.F.15B2.F.15B2.F$F2.15B.F2.15B.F2.15B.F.15B2.F.
15B2.F$F2.7BA3BA3B.F2.15B.F2.7BA7B.F.7B2A6B2.F.7B2A6B2.F$F2.7BA3BA3B.
F2.6B3A6B.F2.6B4A5B.F.7BA2BA4B2.F.6B6A3B2.F$F2.6BABA6B.F2.5BA2BAB2A3B
.F2.5BA2B2A5B.F.6BA3B2A3B2.F.5BA3BA5B2.F$F2.5B3A2B2A3B.F2.5B3A7B.F2.
5BA5BA3B.F.5B3A2B2A3B2.F.5BA4B2A3B2.F$F2.15B.F2.6B5A4B.F2.5BA4BA4B.F.
6B2A7B2.F.5BA2BA6B2.F$F2.8B2A5B.F2.8B2A5B.F2.6BA8B.F.7BA7B2.F.15B2.F$
F2.8B2A5B.F2.7BABA5B.F2.7BABA5B.F.7B2A6B2.F.7B2A6B2.F$F2.7BA7B.F2.8BA
6B.F2.7B2A6B.F.15B2.F.7B2A6B2.F$F2.15B.F2.6BA8B.F2.6B2A7B.F.7BA7B2.F.
7BA7B2.F$F2.5B2A2BA5B.F2.4B3A8B.F2.4BA2BA7B.F.6BABA6B2.F.5B3A7B2.F$F
2.4B2A9B.F2.4B3A8B.F2.3BA2BA8B.F.4B2A9B2.F.3B2AB2A7B2.F$F2.3BA11B.F2.
3BA11B.F2.3BA11B.F.3B2ABA8B2.F.3BA2BA8B2.F$F2.4B2A9B.F2.4BA10B.F2.3B
3A9B.F.4BABA8B2.F.3B2AB2A7B2.F$F2.8BA6B.F2.4B2A9B.F2.4B2A9B.F.7BA7B2.
F.5B3A7B2.F$F2.4BA10B.F2.15B.F2.3BABA9B.F.4BA2BA7B2.F.3B2A10B2.F$F2.
3BA11B.F2.3B2A10B.F2.3B3A9B.F.3B2A10B2.F.3B3A9B2.F$F2.4BA2BA7B.F2.4B
2AB2A6B.F2.3BAB2A8B.F.4BA10B2.F.3B3A9B2.F$F2.5B4A6B.F2.5BA9B.F2.4B3A
8B.F.5BABA7B2.F.6BA8B2.F$F2.7B2A6B.F2.15B.F2.15B.F.7BA7B2.F.7B2A6B2.F
$F2.8B2A5B.F2.9BA5B.F2.6BA8B.F.6B2A7B2.F.5BA9B2.F$F2.5B3A7B.F2.5B3A7B
.F2.5B4A6B.F.5B3ABA5B2.F.5BABA7B2.F$F2.5BA2B2A5B.F2.4BA3BA6B.F2.3B2A
3BA6B.F.4BA4BA5B2.F.4BA4BA5B2.F$F2.4BAB2A7B.F2.3B2ABA2BA5B.F2.3B2A2BA
7B.F.3BAB2ABA6B2.F.3BAB3A7B2.F$F2.3B2ABABA6B.F2.3BA2BA8B.F2.2BA3BA8B.
F.3BA2BA8B2.F.3BA11B2.F$F2.4B2A9B.F2.3B2AB2A7B.F2.3B2A10B.F.4B3A8B2.F
.3BA2BA8B2.F$F2.6BA8B.F2.5B3A7B.F2.4BA3BA6B.F.4B2A9B2.F.4BA10B2.F$F2.
7B2A6B.F2.6BABA6B.F2.8BA6B.F.6BA2BA5B2.F.6BA2BA5B2.F$F2.6BABA2BA3B.F
2.6BAB3A4B.F2.5B2AB3A4B.F.6B6A3B2.F.5B3A3BA3B2.F$F2.5BA3BABA3B.F2.5BA
5BA3B.F2.5BA5BA3B.F.5BA3BA2BA2B2.F.5BA5BA3B2.F$F2.6B5A4B.F2.6B2AB2A4B
.F2.5B3A2BA4B.F.6BABA6B2.F.5B2AB2A5B2.F$F2.7BA7B.F2.6BA8B.F2.6B2A7B.F
.6BABA6B2.F.8BA6B2.F$F2.8BA6B.F2.15B.F2.15B.F.8B2A5B2.F.7B3A5B2.F$F2.
10BA4B.F2.8B2A5B.F2.8B2A5B.F.10BA4B2.F.8B2A5B2.F$F2.6B3A6B.F2.6B3A6B.
F2.6B4A5B.F.7BA7B2.F.6BA8B2.F$F2.5BABA7B.F2.5BA9B.F2.5BA2BA6B.F.5B2A
3BA4B2.F.5B2A8B2.F$F2.4BA2BA7B.F2.4BA2BA7B.F2.3B2A2BA7B.F.4BA10B2.F.
4B2A9B2.F$F2.4B3A8B.F2.3B2AB2A7B.F2.3B2AB3A6B.F.3BA11B2.F.3B2A10B2.F$
F2.4BABA8B.F2.4BA2BA7B.F2.3B3AB2A6B.F.4BA10B2.F.15B2.F$F2.5B2A8B.F2.
7BA7B.F2.5B3A7B.F.15B2.F.4B2A9B2.F$F2.4B3A8B.F2.4BABA8B.F2.3B2AB2A7B.
F.4B2A9B2.F.4BA10B2.F$F2.4BA10B.F2.3B2ABA8B.F2.3BA2BA8B.F.3BA11B2.F.
3BA11B2.F$F2.4BA2BA7B.F2.4B2A9B.F2.3B2AB2A7B.F.4B2A3BA5B2.F.4B3A8B2.F
$F2.5BA9B.F2.6BABA6B.F2.5BAB2A6B.F.5B2A8B2.F.4B3A8B2.F$F2.7BAB2A4B.F
2.8B3A4B.F2.7B4A4B.F.7BA3BA3B2.F.6B3A6B2.F$F2.9B2A4B.F2.11BA3B.F2.8BA
2BA3B.F.8B2A2BA2B2.F.8B2A2BA2B2.F$F2.9B2A4B.F2.8BABA4B.F2.10B2A3B.F.
10B3A2B2.F.12BA2B2.F$F2.5BA2BA6B.F2.8BABA4B.F2.10BA4B.F.10B2A3B2.F.5B
2A2BA5B2.F$F2.5BA2B2A5B.F2.4B2AB3A5B.F2.4B2ABA2BA4B.F.4B4A2B2A3B2.F.
4B4A7B2.F$F2.4BA3BA6B.F2.4BA3B2A5B.F2.3B2ABA2BA5B.F.4BA2B4A4B2.F.3BA
3BA7B2.F$F2.5B3A7B.F2.4BA2BA7B.F2.4B2A2BA6B.F.4B2A3B2A4B2.F.4B2A5BA3B
2.F$F2.5B2A8B.F2.5BA9B.F2.6B3A6B.F.10BA4B2.F.5BA4BA4B2.F$F2.7BA7B.F2.
7B2A6B.F2.6B3A6B.F.6BA2BA5B2.F.15B2.F$F2.7B2A6B.F2.7B2A6B.F2.6BA8B.F.
7BA7B2.F.6B2A7B2.F$F2.15B.F2.7BA7B.F2.7BABA5B.F.7B2A6B2.F.7BA7B2.F$F
2.8B3A4B.F2.8BABA4B.F2.7B2A6B.F.8B3A4B2.F.7B3A5B2.F$F2.9B2A4B.F2.8BAB
A4B.F2.10BA4B.F.15B2.F.10BA4B2.F$F2.15B.F2.7B3A5B.F2.15B.F.10BA4B2.F.
15B2.F$F2.6B3A6B.F2.6BABA6B.F2.6BAB2A5B.F.15B2.F.6BA8B2.F$F2.6B3A6B.F
2.5BA9B.F2.5BA9B.F.5B3A2BA4B2.F.5B3A7B2.F$F2.5BAB2AB2A3B.F2.4BA6BA3B.
F2.4B2A4BA4B.F.4BABA4BA3B2.F.4BA4BABA3B2.F$F2.4B3A2B3A3B.F2.4BA3B2ABA
3B.F2.3B2A4BABA3B.F.4B3A2B2ABA2B2.F.4BA3B2A2BA2B2.F$F2.5B2A8B.F2.4BAB
A3BA4B.F2.7BAB2A4B.F.5B3AB3A3B2.F.4BA10B2.F$F2.15B.F2.6BA8B.F2.5B2A8B
.F.7B4A4B2.F.5BA5BA3B2.F$F2.7BA7B.F2.7B2A6B.F2.8BA6B.F.6B2A7B2.F.9BA
5B2.F$F2.7B2A6B.F2.6B3A6B.F2.6BABA6B.F.6B2A7B2.F.6B2A7B2.F$F2.7BA7B.F
2.6BA8B.F2.5B2A8B.F.15B2.F.6BA8B2.F$F2.7B2A6B.F2.6BA8B.F2.5B3A7B.F.6B
ABA6B2.F.7BA7B2.F$F2.7B2A6B.F2.6BA8B.F2.15B.F.7BA7B2.F.7BA7B2.F$F2.7B
3A5B.F2.15B.F2.15B.F.15B2.F.7B2A6B2.F$F2.8B2A5B.F2.6BA3BA4B.F2.6B2A7B
.F.6BAB2A5B2.F.7BA7B2.F$F2.6B4A5B.F2.6B2A2BA4B.F2.5B3AB2A4B.F.6BA8B2.
F.5B2A8B2.F$F2.5BA4BA4B.F2.5BA3BA5B.F2.5BABA7B.F.5BA2B2A5B2.F.5BA2B2A
5B2.F$F2.6B2A7B.F2.6BA8B.F2.5B2A8B.F.5B2ABA6B2.F.5B5A5B2.F$F2.15B.F2.
5BABA7B.F2.5BABA7B.F.15B2.F.8BA6B2.F$F2.5B2A2B2A4B.F2.5B2A2B2A4B.F2.
4B2A4BA4B.F.5B2AB3A4B2.F.5B4ABA4B2.F$F2.5BA3BA5B.F2.4BA2B4A4B.F2.4BA
2B2ABA4B.F.5BA2B2ABA3B2.F.4B2ABA3BA3B2.F$F2.5B3A7B.F2.5B2A8B.F2.5B2AB
2A5B.F.5BA3B2A4B2.F.5B2A8B2.F$F2.15B.F2.6BA8B.F2.5B2A8B.F.6BA2BA5B2.F
.15B2.F$F2.15B.F2.15B.F2.7BA7B.F.8B2A5B2.F.9BA5B2.F$F2.8BABA4B.F2.7B
2ABA4B.F2.7B2A6B.F.7B2A6B2.F.7BA7B2.F$F2.7B3ABA3B.F2.7BA3BA3B.F2.7BAB
ABA3B.F.8BABA4B2.F.7B2ABA4B2.F$F2.5BA3B3A3B.F2.9BABA3B.F2.4BA3B2ABA3B
.F.4B2A3B2A4B2.F.4B2A3B2A4B2.F$F2.4BA10B.F2.3B3A3B2A4B.F2.3B2A10B.F.
4B2A9B2.F.3BA11B2.F$F2.3B2A3BA6B.F2.3BA4B2A5B.F2.3BA11B.F.4BA10B2.F.
3BA11B2.F$F2.4B2ABAB2A4B.F2.7BAB2A4B.F2.4BA2BA7B.F.4B4A7B2.F.3B2AB3A
6B2.F$F2.4B2ABA2BA4B.F2.4B2A2B3A4B.F2.4B2ABA2BA4B.F.4BA3B2A5B2.F.4BAB
AB2A5B2.F$F2.15B.F2.5BABA7B.F2.4B2ABA2BA4B.F.8BA2B2A2B2.F.7B2A3BA2B2.
F$F2.6B2A2BA4B.F2.6B2ABA5B.F2.5BABAB2A4B.F.6BA2B4A2B2.F.5B2AB2A5B2.F$
F2.5BA2BABA4B.F2.5BA2BAB2A3B.F2.5BA4BA4B.F.5B3A2B2A3B2.F.4BA2BABA5B2.
F$F2.4BA2BA2BA4B.F2.4BA2B2A6B.F2.4BA10B.F.4B2A5BA3B2.F.4B2A3BABA3B2.F
$F2.5B2A2B3A3B.F2.4BAB2AB3A3B.F2.3B2ABA2BABA3B.F.9B2A4B2.F.4B2A2BA2BA
3B2.F$F2.4BABA8B.F2.4BABA2BABA3B.F2.3B2A3B2ABA3B.F.3BA2BAB3A4B2.F.8BA
6B2.F$F2.4B2A4BA4B.F2.4B3A8B.F2.3BA3BA7B.F.4BA4BA5B2.F.3B2A10B2.F$F2.
7BA7B.F2.4B3A8B.F2.4BA10B.F.4B2A3BA5B2.F.4B3A2B2A4B2.F$F2.5BA2BA6B.F
2.6BAB2A5B.F2.4BA3B2A5B.F.5BAB3A5B2.F.4B2ABA7B2.F$F2.6BABAB2A3B.F2.5B
3AB3A3B.F2.5B3A3BA3B.F.7B3ABA3B2.F.6B2AB2A4B2.F$F2.5BA5BA3B.F2.4BA5B
2A3B.F2.4B2A5BA3B.F.4BA10B2.F.7BAB2A4B2.F$F2.4B4A7B.F2.3BA3B2A6B.F2.
3B2A10B.F.3BA2BA2BA5B2.F.3B4ABA6B2.F$F2.3B2A2BABA5B.F2.3BA11B.F2.2B2A
3B3A5B.F.3BA2B3A2BA3B2.F.3BA4B3A4B2.F$F2.4BA2B2A2BA3B.F2.3B2ABA2B2A4B
.F2.4B2AB4A4B.F.4B3ABA2BA3B2.F.3BA2BABA6B2.F$F2.7B2A2BA3B.F2.2B2A2BAB
2A5B.F2.5BA9B.F18.F18.F!

This was with:

Code: Select all

$ rlife llsss 2c5-s2s '@bg:15' --filters wcaf --constraint unstaggered_max_height

I will leave the computer that did this to go on to height 11 and presumably find 34P5H2V0.

[Sokwe]

I was able to confirm this (no height 10 unstaggered 2c/5 ships) with LLSSS.

Excellent! I was always just a little nervous that I might have messed up somehow when I manually split the search state in order to run this search in WLS 15 years ago. This makes me a lot more confident in the result.

2c/5 [staggered] height 9.4 filled memory (even 120G) and died.

If possible, I'm still curious to know what the minimum staggered height is, although I want to make sure that I understand it correctly in this case. Does the following spaceship (found by Hartmut Holzwart in 2008) have staggered height 9.6?

Code: Select all

x = 30, y = 10, rule = B3/S23
4bo$3b3o$3bo2bo6b2o3bo$4bo2bobob2obob2ob2o6bo$3bobobob2o4bobob2o5b3o$
2b2o2b2o2b2o4bo3bob4o2b2o$3bo3bo8bo4bo3bo2bo$b8o12bob2o3bo$obob2ob4o
17bo$obo6b2o15b2o!

In generations 0 and 1 the ship stays in a height-10 bounding box. In generation 2 the ship is still height 10, but shifted up one row. In generations 3 and 4 the ship has height 9 and stays in the same height-9 bounding box, which itself is contained within the height-10 bounding box of generation 2. I was thinking that if the frame moves on generation 2, then the ship would be height 10 for three generations, followed by height 9 for two generations, giving staggered height 9.6, but I wasn't sure if the frame move would be allowed to be between two height-10 generations while still maintaining a staggered height less than 10. Basically, my guesses for the staggered height of the above ship are either 9.6 or 10. Could it instead be 9.8?

Are the spaceships posted by Stanley Dodd here considered to have staggered height 9.8?

[amling]

2c/5 [staggered] height 9.4 filled memory (even 120G) and died.

If possible, I'm still curious to know what the minimum staggered height is, although I want to make sure that I understand it correctly in this case. Does the following spaceship (found by Hartmut Holzwart in 2008) have staggered height 9.6?

Code: Select all

x = 30, y = 10, rule = B3/S23
4bo$3b3o$3bo2bo6b2o3bo$4bo2bobob2obob2ob2o6bo$3bobobob2o4bobob2o5b3o$
2b2o2b2o2b2o4bo3bob4o2b2o$3bo3bo8bo4bo3bo2bo$b8o12bob2o3bo$obob2ob4o
17bo$obo6b2o15b2o!

In generations 0 and 1 the ship stays in a height-10 bounding box. In generation 2 the ship is still height 10, but shifted up one row. In generations 3 and 4 the ship has height 9 and stays in the same height-9 bounding box, which itself is contained within the height-10 bounding box of generation 2. I was thinking that if the frame moves on generation 2, then the ship would be height 10 for three generations, followed by height 9 for two generations, giving staggered height 9.6, but I wasn't sure if the frame move would be allowed to be between two height-10 generations while still maintaining a staggered height less than 10. Basically, my guesses for the staggered height of the above ship are either 9.6 or 10. Could it instead be 9.8?

Are the spaceships posted by Stanley Dodd here considered to have staggered height 9.8?

Minimum 2c/5 unstaggered height is still on my radar and another computer had already been started on it. I did notice that moebius has already answered this positively for 9.4 earlier this year in this post. As far as I can guess, their "phases" corresponds exactly to what I was counting, namely W rows in 2c5-f2b, only I was scaling down by 5x for consistency with apparent heights in a single generation (so "9" is 45 W rows is 9 rows in each generation).

My height 9.4 search so far has found these three ships:

Code: Select all

x = 91, y = 97, rule = LifeHistory
F2.14B.F2.14B.F2.14B.F.14B2.F.14B2.F$F2.14B.F2.14B.F2.14B.F.14B2.F.
14B2.F$F2.6BA3BA3B.F2.14B.F2.6BA7B.F.6B2A6B2.F.6B2A6B2.F$F2.6BA3BA3B.
F2.5B3A6B.F2.5B4A5B.F.6BA2BA4B2.F.5B6A3B2.F$F2.5BABA6B.F2.4BA2BAB2A3B
.F2.4BA2B2A5B.F.5BA3B2A3B2.F.4BA3BA5B2.F$F2.4B3A2B2A3B.F2.4B3A7B.F2.
4BA5BA3B.F.4B3A2B2A3B2.F.4BA4B2A3B2.F$F2.14B.F2.5B5A4B.F2.4BA4BA4B.F.
5B2A7B2.F.4BA2BA6B2.F$F2.7B2A5B.F2.7B2A5B.F2.5BA8B.F.6BA7B2.F.14B2.F$
F2.7B2A5B.F2.6BABA5B.F2.6BABA5B.F.6B2A6B2.F.6B2A6B2.F$F2.6BA7B.F2.7BA
6B.F2.6B2A6B.F.14B2.F.6B2A6B2.F$F2.14B.F2.5BA8B.F2.5B2A7B.F.6BA7B2.F.
6BA7B2.F$F2.4B2A2BA5B.F2.3B3A8B.F2.3BA2BA7B.F.5BABA6B2.F.4B3A7B2.F$F
2.3B2A9B.F2.3B3A8B.F2.2BA2BA8B.F.3B2A9B2.F.2B2AB2A7B2.F$F2.2BA11B.F2.
2BA11B.F2.2BA11B.F.2B2ABA8B2.F.2BA2BA8B2.F$F2.3B2A9B.F2.3BA10B.F2.2B
3A9B.F.3BABA8B2.F.2B2AB2A7B2.F$F2.8BA5B.F2.3B2A9B.F2.3B2A9B.F.6BA7B2.
F.4B3A7B2.F$F2.3BA10B.F2.14B.F2.2BABA9B.F.3BA2BA7B2.F.2B5A7B2.F$F2.2B
A11B.F2.2B2A10B.F2.2B3A9B.F.2B2ABA8B2.F.2B2A2B2A6B2.F$F2.3BA2BA3BA3B.
F2.3B2AB2ABA4B.F2.2BABAB2A6B.F.3BA3B2A5B2.F.2B2ABAB3A4B2.F$F2.4B3ABAB
A3B.F2.4BABA7B.F2.3B2ABABA5B.F.4B2ABAB2A3B2.F.4BA2BABA4B2.F$F2.6BABA
5B.F2.6BABA5B.F2.6BAB2A4B.F.7BA6B2.F.5BABA6B2.F$F2.6BAB2A4B.F2.6BAB2A
4B.F2.6BAB2A4B.F.6B2AB2A3B2.F.6B2A6B2.F$F2.5B2ABA5B.F2.5B2ABA5B.F2.6B
A7B.F.7BA6B2.F.5BABA6B2.F$F2.6BABA5B.F2.4BABAB2A4B.F2.3B2ABAB2A4B.F.
4B2ABAB2A3B2.F.4B2ABAB2A3B2.F$F2.3B2ABA2BA4B.F2.3B2ABA7B.F2.3B2ABABA
5B.F.3BABABAB2A3B2.F.3BABABA6B2.F$F2.3BA2BA7B.F2.2BA3B2A6B.F2.2BA4BA
6B.F.3BABAB3A4B2.F.2B2ABA8B2.F$F2.3B4A7B.F2.3B4A7B.F2.3BA3BA6B.F.3B2A
2B3A4B2.F.3B2ABA7B2.F$F2.14B.F2.4B2A8B.F2.3BA2BA2BA4B.F.8B3A3B2.F.14B
2.F$F2.9BA4B.F2.8B3A3B.F2.8BABA3B.F.8B2ABA2B2.F.14B2.F$F2.8B3A3B.F2.
8B3A3B.F2.7BA2BA3B.F.7B2A5B2.F.7B3A4B2.F$F2.14B.F2.8BA5B.F2.5BAB2A5B.
F.6BA7B2.F.8BA5B2.F$F2.4B2A3BABA2B.F2.4B3A7B.F2.4BABAB2A4B.F.4B4A6B2.
F.4BA3B2A4B2.F$F2.3BAB2ABA5B.F2.3BAB2AB2A4B.F2.2B2A4B2A4B.F.3BA2BAB3A
3B2.F.3B2A4B2A3B2.F$F2.3BA3B2A5B.F2.2B2ABA2BA5B.F2.2B2ABA8B.F.2BA4BAB
A4B2.F.2B2A2B2AB2A3B2.F$F2.3BABABA6B.F2.3BABABABA4B.F2.2B2ABABA6B.F.
3BA2BA7B2.F.3B2ABA2BA4B2.F$F2.4B2ABAB2A3B.F2.4B2ABA6B.F2.4B2ABA6B.F.
4B3AB2A4B2.F.4BABAB2A4B2.F$F2.7BA6B.F2.7BABA4B.F2.7BA6B.F.6BABA5B2.F.
6BA7B2.F$F2.7B2A5B.F2.7BABA4B.F2.6B2AB2A3B.F.7B2A5B2.F.6BA7B2.F$F2.8B
2A4B.F2.7BABA4B.F2.7BA6B.F.7B3A4B2.F.7BABA4B2.F$F2.9BA4B.F2.8B3A3B.F
2.14B.F.14B2.F.8BA5B2.F$F2.10BA3B.F2.9B2A3B.F2.14B.F.14B2.F.14B2.F$F
2.10BA3B.F2.9BA4B.F2.9B2A3B.F.9B2A3B2.F.8BABA3B2.F$F2.8BA5B.F2.7B2A5B
.F2.7B2A5B.F.8B3A3B2.F.7BA2BA3B2.F$F2.7B3A4B.F2.7BA6B.F2.7BA6B.F.7B2A
5B2.F.7B2A5B2.F$F2.8B2A4B.F2.9BA4B.F2.7BA6B.F.14B2.F.7BA6B2.F$F2.7BA
6B.F2.7B2A5B.F2.6B3A5B.F.6BA7B2.F.14B2.F$F2.6BA7B.F2.6B2A6B.F2.5B4A5B
.F.6BA2BA4B2.F.5B2A7B2.F$F2.5BABA6B.F2.4B2A8B.F2.4BA9B.F.5BA8B2.F.4BA
9B2.F$F2.4B2A8B.F2.4B2A8B.F2.3BA2BA7B.F.4B3A7B2.F.4BABA7B2.F$F2.5BABA
6B.F2.4B2A8B.F2.4BA9B.F.5BA8B2.F.4BA9B2.F$F2.6BA7B.F2.6B2A6B.F2.5B4A
5B.F.6BA2BA4B2.F.5B2A7B2.F$F2.7BA6B.F2.7B2A5B.F2.6B3A5B.F.6BA7B2.F.
14B2.F$F2.8B2A4B.F2.9BA4B.F2.7BA6B.F.14B2.F.7BA6B2.F$F2.7B3A4B.F2.7BA
6B.F2.7BA6B.F.7B2A5B2.F.7B2A5B2.F$F2.8BA5B.F2.7B2A5B.F2.7B2A5B.F.8B3A
3B2.F.7BA2BA3B2.F$F2.10BA3B.F2.9BA4B.F2.9B2A3B.F.9B2A3B2.F.8BABA3B2.F
$F2.10BA3B.F2.9B2A3B.F2.14B.F.14B2.F.14B2.F$F2.9BA4B.F2.8B3A3B.F2.14B
.F.14B2.F.8BA5B2.F$F2.8B2A4B.F2.7BABA4B.F2.7BA6B.F.7B3A4B2.F.7BABA4B
2.F$F2.7B2A5B.F2.7BABA4B.F2.6B2AB2A3B.F.7B2A5B2.F.6BA7B2.F$F2.7BA6B.F
2.7BABA4B.F2.7BA6B.F.6BABA5B2.F.6BA7B2.F$F2.4B2ABAB2A3B.F2.4B2ABA6B.F
2.4B2ABA6B.F.4B3AB2A4B2.F.4BABAB2A4B2.F$F2.3BABABA6B.F2.3BABABABA4B.F
2.2B2ABABA6B.F.3BA2BA7B2.F.3B2ABA2BA4B2.F$F2.3BA3B2A5B.F2.2B2ABA2BA5B
.F2.2B2ABA8B.F.2BA4BABA4B2.F.2B2A2B2AB2A3B2.F$F2.3BAB2ABA5B.F2.3BAB2A
B2A4B.F2.2B2A4B2A4B.F.3BA2BAB3A3B2.F.3B2A4B2A3B2.F$F2.4B2A3BABA2B.F2.
4B3A7B.F2.4BABAB2A4B.F.4B4A6B2.F.4BA3B2A4B2.F$F2.14B.F2.8BA5B.F2.5BAB
2A5B.F.6BA7B2.F.8BA5B2.F$F2.8B3A3B.F2.8B3A3B.F2.7BA2BA3B.F.7B2A5B2.F.
7B3A4B2.F$F2.9BA4B.F2.8B3A3B.F2.8BABA3B.F.8B2ABA2B2.F.14B2.F$F2.14B.F
2.4B2A8B.F2.3BA2BA2BA4B.F.8B3A3B2.F.14B2.F$F2.3B4A7B.F2.3B4A7B.F2.3BA
3BA6B.F.3B2A2B3A4B2.F.3B2ABA7B2.F$F2.3BA2BA7B.F2.2BA3B2A6B.F2.2BA4BA
6B.F.3BABAB3A4B2.F.2B2ABA8B2.F$F2.3B2ABA2BA4B.F2.3B2ABA7B.F2.3B2ABABA
5B.F.3BABABAB2A3B2.F.3BABABA6B2.F$F2.6BABA5B.F2.4BABAB2A4B.F2.3B2ABAB
2A4B.F.4B2ABAB2A3B2.F.4B2ABAB2A3B2.F$F2.5B2ABA5B.F2.5B2ABA5B.F2.6BA7B
.F.7BA6B2.F.5BABA6B2.F$F2.6BAB2A4B.F2.6BAB2A4B.F2.6BAB2A4B.F.6B2AB2A
3B2.F.6B2A6B2.F$F2.6BABA5B.F2.6BABA5B.F2.6BAB2A4B.F.7BA6B2.F.5BABA6B
2.F$F2.4B3ABABA3B.F2.4BABA7B.F2.3B2ABABA5B.F.4B2ABAB2A3B2.F.4BA2BABA
4B2.F$F2.3BA2BA3BA3B.F2.3B2AB2ABA4B.F2.2BABAB2A6B.F.3BA3B2A5B2.F.2B2A
BAB3A4B2.F$F2.2BA11B.F2.2B2A10B.F2.2B3A9B.F.2B2ABA8B2.F.2B2A2B2A6B2.F
$F2.3BA10B.F2.14B.F2.2BABA9B.F.3BA2BA7B2.F.2B5A7B2.F$F2.8BA5B.F2.3B2A
9B.F2.3B2A9B.F.6BA7B2.F.4B3A7B2.F$F2.3B2A9B.F2.3BA10B.F2.2B3A9B.F.3BA
BA8B2.F.2B2AB2A7B2.F$F2.2BA11B.F2.2BA11B.F2.2BA11B.F.2B2ABA8B2.F.2BA
2BA8B2.F$F2.3B2A9B.F2.3B3A8B.F2.2BA2BA8B.F.3B2A9B2.F.2B2AB2A7B2.F$F2.
4B2A2BA5B.F2.3B3A8B.F2.3BA2BA7B.F.5BABA6B2.F.4B3A7B2.F$F2.14B.F2.5BA
8B.F2.5B2A7B.F.6BA7B2.F.6BA7B2.F$F2.6BA7B.F2.7BA6B.F2.6B2A6B.F.14B2.F
.6B2A6B2.F$F2.7B2A5B.F2.6BABA5B.F2.6BABA5B.F.6B2A6B2.F.6B2A6B2.F$F2.
7B2A5B.F2.7B2A5B.F2.5BA8B.F.6BA7B2.F.14B2.F$F2.14B.F2.5B5A4B.F2.4BA4B
A4B.F.5B2A7B2.F.4BA2BA6B2.F$F2.4B3A2B2A3B.F2.4B3A7B.F2.4BA5BA3B.F.4B
3A2B2A3B2.F.4BA4B2A3B2.F$F2.5BABA6B.F2.4BA2BAB2A3B.F2.4BA2B2A5B.F.5BA
3B2A3B2.F.4BA3BA5B2.F$F2.6BA3BA3B.F2.5B3A6B.F2.5B4A5B.F.6BA2BA4B2.F.
5B6A3B2.F$F2.6BA3BA3B.F2.14B.F2.6BA7B.F.6B2A6B2.F.6B2A6B2.F$F2.14B.F
2.14B.F2.14B.F.14B2.F.14B2.F$F2.14B.F2.14B.F2.14B.F.14B2.F.14B2.F!

Code: Select all

x = 91, y = 105, rule = LifeHistory
F2.14B.F2.14B.F2.14B.F.14B2.F.14B2.F$F2.14B.F2.14B.F2.14B.F.14B2.F.
14B2.F$F2.7B2A5B.F2.6BA3BA3B.F2.14B.F.7BA6B2.F.6B2A6B2.F$F2.6B6A2B.F
2.6BA3BA3B.F2.5B3A6B.F.6B4A4B2.F.6BA2BA4B2.F$F2.5BA3BA4B.F2.5BABA6B.F
2.4BA2BAB2A3B.F.5BA2B2A4B2.F.5BA3B2A3B2.F$F2.5BA4B2A2B.F2.4B3A2B2A3B.
F2.4B3A7B.F.5BA5BA2B2.F.4B3A2B2A3B2.F$F2.5BA2BA5B.F2.14B.F2.5B5A4B.F.
5BA4BA3B2.F.5B2A7B2.F$F2.14B.F2.7B2A5B.F2.7B2A5B.F.6BA7B2.F.6BA7B2.F$
F2.7B2A5B.F2.7B2A5B.F2.6BABA5B.F.7BABA4B2.F.6B2A6B2.F$F2.7B2A5B.F2.6B
A7B.F2.7BA6B.F.7B2A5B2.F.14B2.F$F2.7BA6B.F2.14B.F2.5BA8B.F.6B2A6B2.F.
6BA7B2.F$F2.5B3A6B.F2.4B2A2BA5B.F2.3B3A8B.F.4BA2BA6B2.F.5BABA6B2.F$F
2.3B2AB2A6B.F2.3B2A9B.F2.3B3A8B.F.3BA2BA7B2.F.3B2A9B2.F$F2.3BA2BA7B.F
2.2BA11B.F2.2BA11B.F.3BA10B2.F.2B2ABA8B2.F$F2.3B2AB2A6B.F2.3B2A9B.F2.
3BA10B.F.3B3A8B2.F.3BABA8B2.F$F2.5B3A6B.F2.7BA6B.F2.3B2A9B.F.4B2A8B2.
F.6BA7B2.F$F2.3B2A9B.F2.3BA10B.F2.14B.F.3BABA8B2.F.3BA2BA7B2.F$F2.3B
3A8B.F2.2BA11B.F2.2B2A10B.F.3B3A8B2.F.2B2A10B2.F$F2.3B2ABA7B.F2.3BA3B
A6B.F2.3B2ABA7B.F.3BAB2A7B2.F.3BA2BA7B2.F$F2.5B3A6B.F2.4B2ABA6B.F2.4B
A2BA6B.F.4B2A3BA4B2.F.4B2A8B2.F$F2.7BA6B.F2.7B2A5B.F2.6B3A5B.F.7BA6B
2.F.6BA7B2.F$F2.9BA4B.F2.8BA5B.F2.7B2A5B.F.7BABA4B2.F.6B3A5B2.F$F2.5B
A3BA4B.F2.4BA9B.F2.3B2A9B.F.4BABA7B2.F.5B3A6B2.F$F2.3B2A9B.F2.3B2A9B.
F2.3B3A8B.F.3BA2BA7B2.F.3B2ABA7B2.F$F2.3BA5BA4B.F2.2BA2BA8B.F2.2BA2BA
8B.F.3BA2B2A6B2.F.2B2AB3A6B2.F$F2.3B3A8B.F2.3B2A3BA5B.F2.3BA2BA7B.F.
3B2A2BA6B2.F.3B2AB3A5B2.F$F2.7BABA4B.F2.4B2ABA6B.F2.3BAB2A7B.F.8BA5B
2.F.7B2A5B2.F$F2.6B3A5B.F2.5BA8B.F2.5B2A7B.F.7BA6B2.F.14B2.F$F2.5B3A
6B.F2.4BA9B.F2.4BA9B.F.4B2A8B2.F.4B3A7B2.F$F2.3B2AB2A6B.F2.3BA3BA6B.F
2.3B2A9B.F.3BABA8B2.F.3BABA8B2.F$F2.3B2A9B.F2.3BA3BA6B.F2.2B2A3B2A5B.
F.3BA10B2.F.2B2A10B2.F$F2.5B2A7B.F2.3BAB3A6B.F2.4BA9B.F.3BA10B2.F.4BA
9B2.F$F2.3BA3B2A5B.F2.7B2A5B.F2.2BA11B.F.5BA8B2.F.2B3AB2A6B2.F$F2.2BA
4BA6B.F2.2B3AB3A5B.F2.2BAB3ABA5B.F.2B2A2B3A5B2.F.2B3ABA2BA4B2.F$F2.3B
ABA8B.F2.3B2A9B.F2.2BA4BA6B.F.3BA3B3A4B2.F.2B3ABA3BA3B2.F$F2.4BA9B.F
2.4BA9B.F2.3B2A4BA4B.F.4BA4B2A3B2.F.14B2.F$F2.9BA4B.F2.8B3A3B.F2.8BAB
A3B.F.9BABA2B2.F.9BA4B2.F$F2.8B3A3B.F2.8B3A3B.F2.7BA2BA3B.F.7B2A5B2.F
.7B2A5B2.F$F2.14B.F2.8BA5B.F2.5BAB2A5B.F.6BA7B2.F.8BA5B2.F$F2.4B2A3BA
BA2B.F2.4B3A7B.F2.4BABAB2A4B.F.4B4A6B2.F.4BA3B2A4B2.F$F2.3BAB2ABA5B.F
2.3BAB2AB2A4B.F2.2B2A4B2A4B.F.3BA2BAB3A3B2.F.3B2A4B2A3B2.F$F2.3BA3B2A
5B.F2.2B2ABA2BA5B.F2.2B2ABA8B.F.2BA4BABA4B2.F.2B2A2B2AB2A3B2.F$F2.3BA
BABA6B.F2.3BABABABA4B.F2.2B2ABABA6B.F.3BA2BA7B2.F.3B2ABA2BA4B2.F$F2.
4B2ABAB2A3B.F2.4B2ABA6B.F2.4B2ABA6B.F.4B3AB2A4B2.F.4BABAB2A4B2.F$F2.
7BA6B.F2.7BABA4B.F2.7BA6B.F.6BABA5B2.F.6BA7B2.F$F2.7B2A5B.F2.7BABA4B.
F2.6B2AB2A3B.F.7B2A5B2.F.6BA7B2.F$F2.8B2A4B.F2.7BABA4B.F2.7BA6B.F.7B
3A4B2.F.7BABA4B2.F$F2.9BA4B.F2.8B3A3B.F2.14B.F.14B2.F.8BA5B2.F$F2.10B
A3B.F2.9B2A3B.F2.14B.F.14B2.F.14B2.F$F2.10BA3B.F2.9BA4B.F2.9B2A3B.F.
9B2A3B2.F.8BABA3B2.F$F2.8BA5B.F2.7B2A5B.F2.7B2A5B.F.8B3A3B2.F.7BA2BA
3B2.F$F2.7B3A4B.F2.7BA6B.F2.7BA6B.F.7B2A5B2.F.7B2A5B2.F$F2.8B2A4B.F2.
9BA4B.F2.7BA6B.F.14B2.F.7BA6B2.F$F2.7BA6B.F2.7B2A5B.F2.6B3A5B.F.6BA7B
2.F.14B2.F$F2.6BA7B.F2.6B2A6B.F2.5B4A5B.F.6BA2BA4B2.F.5B2A7B2.F$F2.5B
ABA6B.F2.4B2A8B.F2.4BA9B.F.5BA8B2.F.4BA9B2.F$F2.4B2A8B.F2.4B2A8B.F2.
3BA2BA7B.F.4B3A7B2.F.4BABA7B2.F$F2.5BABA6B.F2.4B2A8B.F2.4BA9B.F.5BA8B
2.F.4BA9B2.F$F2.6BA7B.F2.6B2A6B.F2.5B4A5B.F.6BA2BA4B2.F.5B2A7B2.F$F2.
7BA6B.F2.7B2A5B.F2.6B3A5B.F.6BA7B2.F.14B2.F$F2.8B2A4B.F2.9BA4B.F2.7BA
6B.F.14B2.F.7BA6B2.F$F2.7B3A4B.F2.7BA6B.F2.7BA6B.F.7B2A5B2.F.7B2A5B2.
F$F2.8BA5B.F2.7B2A5B.F2.7B2A5B.F.8B3A3B2.F.7BA2BA3B2.F$F2.10BA3B.F2.
9BA4B.F2.9B2A3B.F.9B2A3B2.F.8BABA3B2.F$F2.10BA3B.F2.9B2A3B.F2.14B.F.
14B2.F.14B2.F$F2.9BA4B.F2.8B3A3B.F2.14B.F.14B2.F.8BA5B2.F$F2.8B2A4B.F
2.7BABA4B.F2.7BA6B.F.7B3A4B2.F.7BABA4B2.F$F2.7B2A5B.F2.7BABA4B.F2.6B
2AB2A3B.F.7B2A5B2.F.6BA7B2.F$F2.7BA6B.F2.7BABA4B.F2.7BA6B.F.6BABA5B2.
F.6BA7B2.F$F2.4B2ABAB2A3B.F2.4B2ABA6B.F2.4B2ABA6B.F.4B3AB2A4B2.F.4BAB
AB2A4B2.F$F2.3BABABA6B.F2.3BABABABA4B.F2.2B2ABABA6B.F.3BA2BA7B2.F.3B
2ABA2BA4B2.F$F2.3BA3B2A5B.F2.2B2ABA2BA5B.F2.2B2ABA8B.F.2BA4BABA4B2.F.
2B2A2B2AB2A3B2.F$F2.3BAB2ABA5B.F2.3BAB2AB2A4B.F2.2B2A4B2A4B.F.3BA2BAB
3A3B2.F.3B2A4B2A3B2.F$F2.4B2A3BABA2B.F2.4B3A7B.F2.4BABAB2A4B.F.4B4A6B
2.F.4BA3B2A4B2.F$F2.14B.F2.8BA5B.F2.5BAB2A5B.F.6BA7B2.F.8BA5B2.F$F2.
8B3A3B.F2.8B3A3B.F2.7BA2BA3B.F.7B2A5B2.F.7B3A4B2.F$F2.9BA4B.F2.8B3A3B
.F2.8BABA3B.F.8B2ABA2B2.F.14B2.F$F2.14B.F2.4B2A8B.F2.3BA2BA2BA4B.F.8B
3A3B2.F.14B2.F$F2.3B4A7B.F2.3B4A7B.F2.3BA3BA6B.F.3B2A2B3A4B2.F.3B2ABA
7B2.F$F2.3BA2BA7B.F2.2BA3B2A6B.F2.2BA4BA6B.F.3BABAB3A4B2.F.2B2ABA8B2.
F$F2.3B2ABA2BA4B.F2.3B2ABA7B.F2.3B2ABABA5B.F.3BABABAB2A3B2.F.3BABABA
6B2.F$F2.6BABA5B.F2.4BABAB2A4B.F2.3B2ABAB2A4B.F.4B2ABAB2A3B2.F.4B2ABA
B2A3B2.F$F2.5B2ABA5B.F2.5B2ABA5B.F2.6BA7B.F.7BA6B2.F.5BABA6B2.F$F2.6B
AB2A4B.F2.6BAB2A4B.F2.6BAB2A4B.F.6B2AB2A3B2.F.6B2A6B2.F$F2.6BABA5B.F
2.6BABA5B.F2.6BAB2A4B.F.7BA6B2.F.5BABA6B2.F$F2.4B3ABABA3B.F2.4BABA7B.
F2.3B2ABABA5B.F.4B2ABAB2A3B2.F.4BA2BABA4B2.F$F2.3BA2BA3BA3B.F2.3B2AB
2ABA4B.F2.2BABAB2A6B.F.3BA3B2A5B2.F.2B2ABAB3A4B2.F$F2.2BA11B.F2.2B2A
10B.F2.2B3A9B.F.2B2ABA8B2.F.2B2A2B2A6B2.F$F2.3BA10B.F2.14B.F2.2BABA9B
.F.3BA2BA7B2.F.2B5A7B2.F$F2.8BA5B.F2.3B2A9B.F2.3B2A9B.F.6BA7B2.F.4B3A
7B2.F$F2.3B2A9B.F2.3BA10B.F2.2B3A9B.F.3BABA8B2.F.2B2AB2A7B2.F$F2.2BA
11B.F2.2BA11B.F2.2BA11B.F.2B2ABA8B2.F.2BA2BA8B2.F$F2.3B2A9B.F2.3B3A8B
.F2.2BA2BA8B.F.3B2A9B2.F.2B2AB2A7B2.F$F2.4B2A2BA5B.F2.3B3A8B.F2.3BA2B
A7B.F.5BABA6B2.F.4B3A7B2.F$F2.14B.F2.5BA8B.F2.5B2A7B.F.6BA7B2.F.6BA7B
2.F$F2.6BA7B.F2.7BA6B.F2.6B2A6B.F.14B2.F.6B2A6B2.F$F2.7B2A5B.F2.6BABA
5B.F2.6BABA5B.F.6B2A6B2.F.6B2A6B2.F$F2.7B2A5B.F2.7B2A5B.F2.5BA8B.F.6B
A7B2.F.14B2.F$F2.14B.F2.5B5A4B.F2.4BA4BA4B.F.5B2A7B2.F.4BA2BA6B2.F$F
2.4B3A2B2A3B.F2.4B3A7B.F2.4BA5BA3B.F.4B3A2B2A3B2.F.4BA4B2A3B2.F$F2.5B
ABA6B.F2.4BA2BAB2A3B.F2.4BA2B2A5B.F.5BA3B2A3B2.F.4BA3BA5B2.F$F2.6BA3B
A3B.F2.5B3A6B.F2.5B4A5B.F.6BA2BA4B2.F.5B6A3B2.F$F2.6BA3BA3B.F2.14B.F
2.6BA7B.F.6B2A6B2.F.6B2A6B2.F$F2.14B.F2.14B.F2.14B.F.14B2.F.14B2.F$F
2.14B.F2.14B.F2.14B.F.14B2.F.14B2.F!

Code: Select all

x = 91, y = 105, rule = LifeHistory
F2.14B.F2.14B.F2.14B.F.14B2.F.14B2.F$F2.14B.F2.14B.F2.14B.F.14B2.F.
14B2.F$F2.6BA3BA3B.F2.14B.F2.6BA7B.F.6B2A6B2.F.6B2A6B2.F$F2.6BA3BA3B.
F2.5B3A6B.F2.5B4A5B.F.6BA2BA4B2.F.5B6A3B2.F$F2.5BABA6B.F2.4BA2BAB2A3B
.F2.4BA2B2A5B.F.5BA3B2A3B2.F.4BA3BA5B2.F$F2.4B3A2B2A3B.F2.4B3A7B.F2.
4BA5BA3B.F.4B3A2B2A3B2.F.4BA4B2A3B2.F$F2.14B.F2.5B5A4B.F2.4BA4BA4B.F.
5B2A7B2.F.4BA2BA6B2.F$F2.7B2A5B.F2.7B2A5B.F2.5BA8B.F.6BA7B2.F.14B2.F$
F2.7B2A5B.F2.6BABA5B.F2.6BABA5B.F.6B2A6B2.F.6B2A6B2.F$F2.6BA7B.F2.7BA
6B.F2.6B2A6B.F.14B2.F.6B2A6B2.F$F2.14B.F2.5BA8B.F2.5B2A7B.F.6BA7B2.F.
6BA7B2.F$F2.4B2A2BA5B.F2.3B3A8B.F2.3BA2BA7B.F.5BABA6B2.F.4B3A7B2.F$F
2.3B2A9B.F2.3B3A8B.F2.2BA2BA8B.F.3B2A9B2.F.2B2AB2A7B2.F$F2.2BA11B.F2.
2BA11B.F2.2BA11B.F.2B2ABA8B2.F.2BA2BA8B2.F$F2.3B2A9B.F2.3BA10B.F2.2B
3A9B.F.3BABA8B2.F.2B2AB2A7B2.F$F2.8BA5B.F2.3B2A9B.F2.3B2A9B.F.6BA7B2.
F.4B3A7B2.F$F2.3BA10B.F2.14B.F2.2BABA9B.F.3BA2BA7B2.F.2B5A7B2.F$F2.2B
A11B.F2.2B2A10B.F2.2B3A9B.F.2B2ABA8B2.F.2B2A2B2A6B2.F$F2.3BA2BA3BA3B.
F2.3B2AB2ABA4B.F2.2BABAB2A6B.F.3BA3B2A5B2.F.2B2ABAB3A4B2.F$F2.4B3ABAB
A3B.F2.4BABA7B.F2.3B2ABABA5B.F.4B2ABAB2A3B2.F.4BA2BABA4B2.F$F2.6BABA
5B.F2.6BABA5B.F2.6BAB2A4B.F.7BA6B2.F.5BABA6B2.F$F2.6BAB2A4B.F2.6BAB2A
4B.F2.6BAB2A4B.F.6B2AB2A3B2.F.6B2A6B2.F$F2.5B2ABA5B.F2.5B2ABA5B.F2.6B
A7B.F.7BA6B2.F.5BABA6B2.F$F2.6BABA5B.F2.4BABAB2A4B.F2.3B2ABAB2A4B.F.
4B2ABAB2A3B2.F.4B2ABAB2A3B2.F$F2.3B2ABA2BA4B.F2.3B2ABA7B.F2.3B2ABABA
5B.F.3BABABAB2A3B2.F.3BABABA6B2.F$F2.3BA2BA7B.F2.2BA3B2A6B.F2.2BA4BA
6B.F.3BABAB3A4B2.F.2B2ABA8B2.F$F2.3B4A7B.F2.3B4A7B.F2.3BA3BA6B.F.3B2A
2B3A4B2.F.3B2ABA7B2.F$F2.14B.F2.4B2A8B.F2.3BA2BA2BA4B.F.8B3A3B2.F.14B
2.F$F2.9BA4B.F2.8B3A3B.F2.8BABA3B.F.8B2ABA2B2.F.14B2.F$F2.8B3A3B.F2.
8B3A3B.F2.7BA2BA3B.F.7B2A5B2.F.7B3A4B2.F$F2.14B.F2.8BA5B.F2.5BAB2A5B.
F.6BA7B2.F.8BA5B2.F$F2.4B2A3BABA2B.F2.4B3A7B.F2.4BABAB2A4B.F.4B4A6B2.
F.4BA3B2A4B2.F$F2.3BAB2ABA5B.F2.3BAB2AB2A4B.F2.2B2A4B2A4B.F.3BA2BAB3A
3B2.F.3B2A4B2A3B2.F$F2.3BA3B2A5B.F2.2B2ABA2BA5B.F2.2B2ABA8B.F.2BA4BAB
A4B2.F.2B2A2B2AB2A3B2.F$F2.3BABABA6B.F2.3BABABABA4B.F2.2B2ABABA6B.F.
3BA2BA7B2.F.3B2ABA2BA4B2.F$F2.4B2ABAB2A3B.F2.4B2ABA6B.F2.4B2ABA6B.F.
4B3AB2A4B2.F.4BABAB2A4B2.F$F2.7BA6B.F2.7BABA4B.F2.7BA6B.F.6BABA5B2.F.
6BA7B2.F$F2.7B2A5B.F2.7BABA4B.F2.6B2AB2A3B.F.7B2A5B2.F.6BA7B2.F$F2.8B
2A4B.F2.7BABA4B.F2.7BA6B.F.7B3A4B2.F.7BABA4B2.F$F2.9BA4B.F2.8B3A3B.F
2.14B.F.14B2.F.8BA5B2.F$F2.10BA3B.F2.9B2A3B.F2.14B.F.14B2.F.14B2.F$F
2.10BA3B.F2.9BA4B.F2.9B2A3B.F.9B2A3B2.F.8BABA3B2.F$F2.8BA5B.F2.7B2A5B
.F2.7B2A5B.F.8B3A3B2.F.7BA2BA3B2.F$F2.7B3A4B.F2.7BA6B.F2.7BA6B.F.7B2A
5B2.F.7B2A5B2.F$F2.8B2A4B.F2.9BA4B.F2.7BA6B.F.14B2.F.7BA6B2.F$F2.7BA
6B.F2.7B2A5B.F2.6B3A5B.F.6BA7B2.F.14B2.F$F2.6BA7B.F2.6B2A6B.F2.5B4A5B
.F.6BA2BA4B2.F.5B2A7B2.F$F2.5BABA6B.F2.4B2A8B.F2.4BA9B.F.5BA8B2.F.4BA
9B2.F$F2.4B2A8B.F2.4B2A8B.F2.3BA2BA7B.F.4B3A7B2.F.4BABA7B2.F$F2.5BABA
6B.F2.4B2A8B.F2.4BA9B.F.5BA8B2.F.4BA9B2.F$F2.6BA7B.F2.6B2A6B.F2.5B4A
5B.F.6BA2BA4B2.F.5B2A7B2.F$F2.7BA6B.F2.7B2A5B.F2.6B3A5B.F.6BA7B2.F.
14B2.F$F2.8B2A4B.F2.9BA4B.F2.7BA6B.F.14B2.F.7BA6B2.F$F2.7B3A4B.F2.7BA
6B.F2.7BA6B.F.7B2A5B2.F.7B2A5B2.F$F2.8BA5B.F2.7B2A5B.F2.7B2A5B.F.8B3A
3B2.F.7BA2BA3B2.F$F2.10BA3B.F2.9BA4B.F2.9B2A3B.F.9B2A3B2.F.8BABA3B2.F
$F2.10BA3B.F2.9B2A3B.F2.14B.F.14B2.F.14B2.F$F2.9BA4B.F2.8B3A3B.F2.14B
.F.14B2.F.8BA5B2.F$F2.8B2A4B.F2.7BABA4B.F2.7BA6B.F.7B3A4B2.F.7BABA4B
2.F$F2.7B2A5B.F2.7BABA4B.F2.6B2AB2A3B.F.7B2A5B2.F.6BA7B2.F$F2.7BA6B.F
2.7BABA4B.F2.7BA6B.F.6BABA5B2.F.6BA7B2.F$F2.4B2ABAB2A3B.F2.4B2ABA6B.F
2.4B2ABA6B.F.4B3AB2A4B2.F.4BABAB2A4B2.F$F2.3BABABA6B.F2.3BABABABA4B.F
2.2B2ABABA6B.F.3BA2BA7B2.F.3B2ABA2BA4B2.F$F2.3BA3B2A5B.F2.2B2ABA2BA5B
.F2.2B2ABA8B.F.2BA4BABA4B2.F.2B2A2B2AB2A3B2.F$F2.3BAB2ABA5B.F2.3BAB2A
B2A4B.F2.2B2A4B2A4B.F.3BA2BAB3A3B2.F.3B2A4B2A3B2.F$F2.4B2A3BABA2B.F2.
4B3A7B.F2.4BABAB2A4B.F.4B4A6B2.F.4BA3B2A4B2.F$F2.14B.F2.8BA5B.F2.5BAB
2A5B.F.6BA7B2.F.8BA5B2.F$F2.8B3A3B.F2.8B3A3B.F2.7BA2BA3B.F.7B2A5B2.F.
7B2A5B2.F$F2.9BA4B.F2.8B3A3B.F2.8BABA3B.F.9BABA2B2.F.9BA4B2.F$F2.4BA
9B.F2.4BA9B.F2.3B2A4BA4B.F.4BA4B2A3B2.F.14B2.F$F2.3BABA8B.F2.3B2A9B.F
2.2BA4BA6B.F.3BA3B3A4B2.F.2B3ABA3BA3B2.F$F2.2BA4BA6B.F2.2B3AB3A5B.F2.
2BAB3ABA5B.F.2B2A2B3A5B2.F.2B3ABA2BA4B2.F$F2.3BA3B2A5B.F2.7B2A5B.F2.
2BA11B.F.5BA8B2.F.2B3AB2A6B2.F$F2.5B2A7B.F2.3BAB3A6B.F2.4BA9B.F.3BA
10B2.F.4BA9B2.F$F2.3B2A9B.F2.3BA3BA6B.F2.2B2A3B2A5B.F.3BA10B2.F.2B2A
10B2.F$F2.3B2AB2A6B.F2.3BA3BA6B.F2.3B2A9B.F.3BABA8B2.F.3BABA8B2.F$F2.
5B3A6B.F2.4BA9B.F2.4BA9B.F.4B2A8B2.F.4B3A7B2.F$F2.6B3A5B.F2.5BA8B.F2.
5B2A7B.F.7BA6B2.F.14B2.F$F2.7BABA4B.F2.4B2ABA6B.F2.3BAB2A7B.F.8BA5B2.
F.7B2A5B2.F$F2.3B3A8B.F2.3B2A3BA5B.F2.3BA2BA7B.F.3B2A2BA6B2.F.3B2AB3A
5B2.F$F2.3BA5BA4B.F2.2BA2BA8B.F2.2BA2BA8B.F.3BA2B2A6B2.F.2B2AB3A6B2.F
$F2.3B2A9B.F2.3B2A9B.F2.3B3A8B.F.3BA2BA7B2.F.3B2ABA7B2.F$F2.5BA3BA4B.
F2.4BA9B.F2.3B2A9B.F.4BABA7B2.F.5B3A6B2.F$F2.9BA4B.F2.8BA5B.F2.7B2A5B
.F.7BABA4B2.F.6B3A5B2.F$F2.7BA6B.F2.7B2A5B.F2.6B3A5B.F.7BA6B2.F.6BA7B
2.F$F2.5B3A6B.F2.4B2ABA6B.F2.4BA2BA6B.F.4B2A3BA4B2.F.4B2A8B2.F$F2.3B
2ABA7B.F2.3BA3BA6B.F2.3B2ABA7B.F.3BAB2A7B2.F.3BA2BA7B2.F$F2.3B3A8B.F
2.2BA11B.F2.2B2A10B.F.3B3A8B2.F.2B2A10B2.F$F2.3B2A9B.F2.3BA10B.F2.14B
.F.3BABA8B2.F.3BA2BA7B2.F$F2.5B3A6B.F2.7BA6B.F2.3B2A9B.F.4B2A8B2.F.6B
A7B2.F$F2.3B2AB2A6B.F2.3B2A9B.F2.3BA10B.F.3B3A8B2.F.3BABA8B2.F$F2.3BA
2BA7B.F2.2BA11B.F2.2BA11B.F.3BA10B2.F.2B2ABA8B2.F$F2.3B2AB2A6B.F2.3B
2A9B.F2.3B3A8B.F.3BA2BA7B2.F.3B2A9B2.F$F2.5B3A6B.F2.4B2A2BA5B.F2.3B3A
8B.F.4BA2BA6B2.F.5BABA6B2.F$F2.7BA6B.F2.14B.F2.5BA8B.F.6B2A6B2.F.6BA
7B2.F$F2.7B2A5B.F2.6BA7B.F2.7BA6B.F.7B2A5B2.F.14B2.F$F2.7B2A5B.F2.7B
2A5B.F2.6BABA5B.F.7BABA4B2.F.6B2A6B2.F$F2.14B.F2.7B2A5B.F2.7B2A5B.F.
6BA7B2.F.6BA7B2.F$F2.5BA2BA5B.F2.14B.F2.5B5A4B.F.5BA4BA3B2.F.5B2A7B2.
F$F2.5BA4B2A2B.F2.4B3A2B2A3B.F2.4B3A7B.F.5BA5BA2B2.F.4B3A2B2A3B2.F$F
2.5BA3BA4B.F2.5BABA6B.F2.4BA2BAB2A3B.F.5BA2B2A4B2.F.5BA3B2A3B2.F$F2.
6B6A2B.F2.6BA3BA3B.F2.5B3A6B.F.6B4A4B2.F.6BA2BA4B2.F$F2.7B2A5B.F2.6BA
3BA3B.F2.14B.F.7BA6B2.F.6B2A6B2.F$F2.14B.F2.14B.F2.14B.F.14B2.F.14B2.
F$F2.14B.F2.14B.F2.14B.F.14B2.F.14B2.F!

I'll leave it run until it hits the memory limit although I'm not sure I expect it to find anything too exciting.

As for counting height of ships directly, for geometries that are not c/N, it's a mess and best not done by hand and eye. I would answer it with to-uwi instead. As an example, let's analyze that one from HH:

Code: Select all

$ cat 1.rle
x = 30, y = 10, rule = B3/S23
4bo$3b3o$3bo2bo6b2o3bo$4bo2bobob2obob2ob2o6bo$3bobobob2o4bobob2o5b3o$
2b2o2b2o2b2o4bo3bob4o2b2o$3bo3bo8bo4bo3bo2bo$b8o12bob2o3bo$obob2ob4o
17bo$obo6b2o15b2o!
$

Thankfully it's already oriented north which is what we want for 2c5-f2b. First, have ingest-1gp make five generations of it:

Code: Select all

$ rlife slices-tool ingest-1gp 2c5-f2b 1.rle --w-size MAX
...
20251031 17:50:01 [INFO] New aligned slice:
20251031 17:50:01 [INFO]    |                                    |                                    | LLuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuRR | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | ......*........................... | .....***.......................... |
20251031 17:50:01 [INFO]    | ......*........................... | ......*........................... | .....***.......................... | .....***.......................... | .....*.*.......................... |
20251031 17:50:01 [INFO]    | .....*.*.......................... | ....**.**......................... | .....*..*......**...*............. | .....*..*......**...*............. | .....*..*.....****.***............ |
20251031 17:50:01 [INFO]    | ....**.**......**...*............. | .......**.....****.***............ | .......*.*....*..*.*.*.......*.... | ......*..*.*.**.*.**.**......*.... | .....***.*.*.**.*.**..*.....***... |
20251031 17:50:01 [INFO]    | ....**..*....**.**.***.......*.... | ....**...*..***.**.*.*......***... | .....*...****.*....*.**.....*.*... | .....*.*.*.**....*.*.**.....***... | ....**.*.*.*..*..*.*.....****..*.. |
20251031 17:50:01 [INFO]    | .......*.*..**.......*....*.***... | ......**.**.*....*.....*....***... | .....***.*..*....**.....*..*...*.. | ....**..**..**....*...*.****..**.. | ....**...*.***...***.**.****...*.. |
20251031 17:50:01 [INFO]    | .......*.*.*..***....****......*.. | .......*.*.*..***.......**..*..*.. | .....*.................***.**.*... | .....*...*........*....*...*..*... | ...*..................**...*.**... |
20251031 17:50:01 [INFO]    | ...*.**.*..***...*.****.*....*.*.. | ....*.***.**.*******....*...*..... | ......****.........*....**..**.... | ...********............*.**...*... | ...*....................*.*..***.. |
20251031 17:50:01 [INFO]    | ...*........*.....*..**....*.*.... | ...*.......***....**.........*.... | ..***..*..**.*.**..*........**.... | ..*.*.**.****.................*... | ..*.........*.................*... |
20251031 17:50:01 [INFO]    | ..**...................*....*..*.. | ..**..................*.....*.*... | ..**........*................*.... | ..*.*......**...............**.... | .....*......*................*.... |
20251031 17:50:01 [INFO]    | ...............................*.. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. | .................................. | .................................. | .................................. |
20251031 17:50:01 [INFO]    | .................................. | .................................. |                                    |                                    |                                    |
...
$

Now save that and map it to UWI:

Code: Select all

$ cat 1.pic
|                                    |                                    | LLuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuRR | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | ......*........................... | .....***.......................... |
| ......*........................... | ......*........................... | .....***.......................... | .....***.......................... | .....*.*.......................... |
| .....*.*.......................... | ....**.**......................... | .....*..*......**...*............. | .....*..*......**...*............. | .....*..*.....****.***............ |
| ....**.**......**...*............. | .......**.....****.***............ | .......*.*....*..*.*.*.......*.... | ......*..*.*.**.*.**.**......*.... | .....***.*.*.**.*.**..*.....***... |
| ....**..*....**.**.***.......*.... | ....**...*..***.**.*.*......***... | .....*...****.*....*.**.....*.*... | .....*.*.*.**....*.*.**.....***... | ....**.*.*.*..*..*.*.....****..*.. |
| .......*.*..**.......*....*.***... | ......**.**.*....*.....*....***... | .....***.*..*....**.....*..*...*.. | ....**..**..**....*...*.****..**.. | ....**...*.***...***.**.****...*.. |
| .......*.*.*..***....****......*.. | .......*.*.*..***.......**..*..*.. | .....*.................***.**.*... | .....*...*........*....*...*..*... | ...*..................**...*.**... |
| ...*.**.*..***...*.****.*....*.*.. | ....*.***.**.*******....*...*..... | ......****.........*....**..**.... | ...********............*.**...*... | ...*....................*.*..***.. |
| ...*........*.....*..**....*.*.... | ...*.......***....**.........*.... | ..***..*..**.*.**..*........**.... | ..*.*.**.****.................*... | ..*.........*.................*... |
| ..**...................*....*..*.. | ..**..................*.....*.*... | ..**........*................*.... | ..*.*......**...............**.... | .....*......*................*.... |
| ...............................*.. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. | .................................. | .................................. | .................................. |
| .................................. | .................................. |                                    |                                    |                                    |
$ rlife grid-tool to-uwi 2c5-f2b < 1.pic
| LLuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuRR |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| ......*........................... |
| ......*........................... |
| ......*........................... |
| .....***.......................... |
| .....***.......................... |
| .....*.*.......................... |
| .....***.......................... |
| ....**.**......................... |
| .....*.*.......................... |
| .....*..*......**...*............. |
| ....**.**......**...*............. |
| .....*..*......**...*............. |
| .......**.....****.***............ |
| .....*..*.....****.***............ |
| .......*.*....*..*.*.*.......*.... |
| ....**..*....**.**.***.......*.... |
| ......*..*.*.**.*.**.**......*.... |
| ....**...*..***.**.*.*......***... |
| .....***.*.*.**.*.**..*.....***... |
| .....*...****.*....*.**.....*.*... |
| .......*.*..**.......*....*.***... |
| .....*.*.*.**....*.*.**.....***... |
| ......**.**.*....*.....*....***... |
| ....**.*.*.*..*..*.*.....****..*.. |
| .....***.*..*....**.....*..*...*.. |
| .......*.*.*..***....****......*.. |
| ....**..**..**....*...*.****..**.. |
| .......*.*.*..***.......**..*..*.. |
| ....**...*.***...***.**.****...*.. |
| .....*.................***.**.*... |
| ...*.**.*..***...*.****.*....*.*.. |
| .....*...*........*....*...*..*... |
| ....*.***.**.*******....*...*..... |
| ...*..................**...*.**... |
| ......****.........*....**..**.... |
| ...*........*.....*..**....*.*.... |
| ...********............*.**...*... |
| ...*.......***....**.........*.... |
| ...*....................*.*..***.. |
| ..***..*..**.*.**..*........**.... |
| ..**...................*....*..*.. |
| ..*.*.**.****.................*... |
| ..**..................*.....*.*... |
| ..*.........*.................*... |
| ..**........*................*.... |
| ...............................*.. |
| ..*.*......**...............**.... |
| .................................. |
| .....*......*................*.... |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
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| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
| .................................. |
$

Here it easy to see the rectangular UVW prism covering it is 49 W rows long so I would have said it is 49/5 = 9.8 rows tall. I leave Stanley Dodd's ships as an exercise for the reader but if you get stuck and can't work it out let me know.

[Sokwe]

I did notice that moebius has already answered this positively for 9.4 earlier this year in this post. As far as I can guess, their "phases" corresponds exactly to what I was counting, namely W rows in 2c5-f2b, only I was scaling down by 5x for consistency with apparent heights in a single generation (so "9" is 45 W rows is 9 rows in each generation).

I completely forgot about these for some reason. It looks like I thought Tim Coe's definition of height might be different from that in LLSSS, so I didn't regard this problem as solved in my mind.

The next thing I'm curious about is the minimum height, both staggered and unstaggered, of a strict even-symmetric 2c/5 spaceship. During a recent test with LLS for an unstaggered height-11 even-symmetric 2c/5 spaceship, I found this partial result which may or may not be completable at this height:

Code: Select all

x = 84, y = 10, rule = B3/S23
2o3bo31bo8bo31bo3b2o$2bobobo18bo10b3ob4ob3o10bo18bobobo$2bo4bo15b2ob2o
2bo4b2ob3o2b3ob2o4bo2b2ob2o15bo4bo$obobo3bo14b2obob4ob2obo10bob2ob4obo
b2o14bo3bobobo$o5bo2bo9b3ob2obobobobo3bob8obo3bobobobob2ob3o9bo2bo5bo$
b2o7bo2b3o2bo3bo2b2obo3bo6bo4bo6bo3bob2o2bo3bo2b3o2bo7b2o$b3o6bobo2b5o
b2o4b2o2b2o3bo10bo3b2o2b2o4b2ob5o2bobo6b3o$2obobob4o6bo9bo2bo4b2o10b2o
4bo2bo9bo6b4obobob2o$b3obo6b3ob2o12bo22bo12b2ob3o6bob3o$o12b2ob2o13b2o
18b2o13b2ob2o12bo!

[amling]

It looks like I thought Tim Coe's definition of height might be different from that in LLSSS, so I didn't regard this problem as solved in my mind.

I thought I remembered some additional historical basis for my belief that Tim's definition matches LLSSS's, which I think traces to this post. In particular those 2c/5 envelopes match and the way they extend one at a time staggering between the phases is pretty good evidence. So too is "There is a natural way to order the phases when the movement amount is relatively prime to the period".

The next thing I'm curious about is the minimum height, both staggered and unstaggered, of a strict even-symmetric 2c/5 spaceship. During a recent test with LLS for an unstaggered height-11 even-symmetric 2c/5 spaceship, I found this partial result which may or may not be completable at this height:

Code: Select all

x = 84, y = 10, rule = B3/S23
2o3bo31bo8bo31bo3b2o$2bobobo18bo10b3ob4ob3o10bo18bobobo$2bo4bo15b2ob2o
2bo4b2ob3o2b3ob2o4bo2b2ob2o15bo4bo$obobo3bo14b2obob4ob2obo10bob2ob4obo
b2o14bo3bobobo$o5bo2bo9b3ob2obobobobo3bob8obo3bobobobob2ob3o9bo2bo5bo$
b2o7bo2b3o2bo3bo2b2obo3bo6bo4bo6bo3bob2o2bo3bo2b3o2bo7b2o$b3o6bobo2b5o
b2o4b2o2b2o3bo10bo3b2o2b2o4b2ob5o2bobo6b3o$2obobob4o6bo9bo2bo4b2o10b2o
4bo2bo9bo6b4obobob2o$b3obo6b3ob2o12bo22bo12b2ob3o6bob3o$o12b2ob2o13b2o
18b2o13b2ob2o12bo!

I tried some trickery (even wildcard init with 2 row all-zero forbid_grid filter) to force a s2s search to start with a nonzero even boundary. This technique works, but for unstaggered envelopes it did not do better on memory and in particular it ran out of memory trying to rule out a height 11 strict even 2c/5 ship. I may yet go back and try it for staggered envelopes as well but I would not be optimistic of it doing better there either. I will also trying continuing (various truncations of) that partial at height 11 unstaggered.

[amling]

I found this partial result which may or may not be completable at this height:

Code: Select all

x = 84, y = 10, rule = B3/S23
2o3bo31bo8bo31bo3b2o$2bobobo18bo10b3ob4ob3o10bo18bobobo$2bo4bo15b2ob2o
2bo4b2ob3o2b3ob2o4bo2b2ob2o15bo4bo$obobo3bo14b2obob4ob2obo10bob2ob4obo
b2o14bo3bobobo$o5bo2bo9b3ob2obobobobo3bob8obo3bobobobob2ob3o9bo2bo5bo$
b2o7bo2b3o2bo3bo2b2obo3bo6bo4bo6bo3bob2o2bo3bo2b3o2bo7b2o$b3o6bobo2b5o
b2o4b2o2b2o3bo10bo3b2o2b2o4b2ob5o2bobo6b3o$2obobob4o6bo9bo2bo4b2o10b2o
4bo2bo9bo6b4obobob2o$b3obo6b3ob2o12bo22bo12b2ob3o6bob3o$o12b2ob2o13b2o
18b2o13b2ob2o12bo!

Even stripped to just the center two columns this is uncompletable with that envelope (LLSSS exhausts it in ~2h and ~81 GB). Longest partial:

Code: Select all

x = 101, y = 68, rule = LifeHistory
F2.4BA2BA8B.F2.3B2A2B2A7B.F2.16B.F.5BA10B2.F.4B2A10B2.F$F2.4BA2BA8B.F
2.3B2A2B2A7B.F2.16B.F.5BA10B2.F.4B2A10B2.F$F2.4B2ABA8B.F2.4B2ABA8B.F
2.3B3A10B.F.5B2A9B2.F.4BABA9B2.F$F2.5BAB2A7B.F2.7B2A7B.F2.5BA10B.F.4B
ABA9B2.F.4BABA9B2.F$F2.4B2ABA8B.F2.3BABAB2A7B.F2.4BA4BA6B.F.4B2A10B2.
F.3B2ABA9B2.F$F2.3B2A11B.F2.3BA3B2A7B.F2.2B2A12B.F.3BA2BA9B2.F.3BA2B
2A8B2.F$F2.4B4AB2A5B.F2.3BA2BA2B2A5B.F2.3B2ABA3BA5B.F.3BAB2AB2ABA4B2.
F.3BA2B2A2BA5B2.F$F2.5BA4BA5B.F2.4BA2BAB2A5B.F2.4BA2B4A5B.F.4B2A5BA4B
2.F.4BA3BABA5B2.F$F2.6BA9B.F2.5B2A9B.F2.5B2AB2A6B.F.6B2A8B2.F.5B2A9B
2.F$F2.6BA9B.F2.6BABA7B.F2.8B2A6B.F.11BA4B2.F.16B2.F$F2.7B3A2BA3B.F2.
6B4A6B.F2.5B2A2BA6B.F.6B2A2BA5B2.F.6B3AB2A4B2.F$F2.6BA2BA2BA3B.F2.5BA
3BA2BA3B.F2.5BA3BABA4B.F.6BAB3A5B2.F.5BA2B4A4B2.F$F2.5B3A2B2A4B.F2.5B
ABA2B2A4B.F2.6BABA2BA4B.F.6B2A3BA4B2.F.5B2A9B2.F$F2.6BA9B.F2.9B2A5B.F
2.5BA10B.F.6BA2BA6B2.F.5BA10B2.F$F2.6B4A6B.F2.5B6A5B.F2.5B4A2BA4B.F.
6B3A7B2.F.6B3A7B2.F$F2.5BA3B2A5B.F2.5BA4BA5B.F2.10BA5B.F.11BA4B2.F.5B
A2BA7B2.F$F2.5B4A7B.F2.4B5A7B.F2.4BAB4A6B.F.4B2ABA3BA4B2.F.4B3A3B2A4B
2.F$F2.4BA3BA7B.F2.4BA3BA7B.F2.3B2ABAB2A6B.F.4BA2BA2BA5B2.F.3BA3BA8B
2.F$F2.5B3A8B.F2.4BA3BA7B.F2.4B2A10B.F.4B3A9B2.F.4B3A9B2.F$F2.5B3A8B.
F2.5BA10B.F2.16B.F.16B2.F.5BA10B2.F$F2.8B2A6B.F2.9BA6B.F2.8BA7B.F.8BA
7B2.F.8BA7B2.F$F2.7BABA6B.F2.7BABA6B.F2.6B2A8B.F.7BABA6B2.F.7B2A7B2.F
$F2.7BA8B.F2.6B2A8B.F2.6B2A8B.F.6BA9B2.F.6B2A8B2.F$F2.7BABA6B.F2.7BAB
A6B.F2.6B3A7B.F.7BABA6B2.F.7B2A7B2.F$F2.8B2A6B.F2.16B.F2.16B.F.8BA7B
2.F.8BA7B2.F$F2.9B2A5B.F2.10BA5B.F2.16B.F.16B2.F.16B2.F$F2.5BA2BA2BA
4B.F2.4B2A2BA2BA4B.F2.4BA3BA2BA4B.F.8BA7B2.F.8B2A6B2.F$F2.4B5A2BA4B.F
2.4B8A4B.F2.3BA2B2A3BA4B.F.4B2A2B2ABA4B2.F.3B3AB4A5B2.F$F2.3BA6BA5B.F
2.3BA5BA6B.F2.3BA5BA6B.F.3B2ABA2BA6B2.F.3BA2BA9B2.F$F2.4B2AB2A7B.F2.
4B2ABA8B.F2.3BAB2ABA7B.F.4BAB5A5B2.F.3B2AB2A8B2.F$F2.5B2A9B.F2.4B2A2B
A7B.F2.4B2A2BA7B.F.5BA3B2A5B2.F.5BA5BA4B2.F$F2.7BA3B2A3B.F2.7B2A7B.F
2.6BA2BA6B.F.6B2A2BA5B2.F.6B2A2BA5B2.F$F2.7B2A7B.F2.7B2A7B.F2.7B2A7B.
F.8B2A6B2.F.10BA5B2.F$F2.16B.F2.16B.F2.16B.F.8B2A6B2.F.7BA8B2.F$F2.
16B.F2.16B.F2.7BA8B.F.8BA7B2.F.16B2.F$F2.6B2A8B.F2.6B3A7B.F2.6BABA7B.
F.6B3A7B2.F.6BA9B2.F$F2.5BAB2A7B.F2.5BAB2A7B.F2.4B2A10B.F.5BA2B2A6B2.
F.5B2A2BA6B2.F$F2.5BA3BA6B.F2.4B2A3B2A5B.F2.4B2ABABA6B.F.4BA3BA7B2.F.
4B2A2BA7B2.F$F2.5BA3BABA4B.F2.5BA2BA7B.F2.4B5A7B.F.5BA4BA5B2.F.5B4ABA
5B2.F$F2.6B2A3BA4B.F2.6BABA7B.F2.8BA7B.F.6B2AB2A5B2.F.6BA2B2A5B2.F$F
2.9BA6B.F2.8B2ABA4B.F2.10BA5B.F.16B2.F.8BA7B2.F$F2.9B3A4B.F2.8B2A6B.F
2.7BA8B.F.9B2A5B2.F.9B2A5B2.F$F2.9BA6B.F2.8B2A6B.F2.8B2A6B.F.9BA6B2.F
.9BA6B2.F$F2.9BA6B.F2.16B.F2.16B.F.10BA5B2.F.9B2A5B2.F$F2.16B.F2.8B2A
6B.F2.7BABA6B.F.9BA6B2.F.9B2A5B2.F$F2.7B2ABA5B.F2.7B3A6B.F2.7BA8B.F.
7B3A6B2.F.7BABA6B2.F$F2.7B2A7B.F2.6BA3B2A4B.F2.6BA4BA4B.F.7BA8B2.F.6B
2ABA6B2.F$F2.7B2AB2A4B.F2.7B2AB2A4B.F2.6BABA3BA3B.F.7BABA2B2A2B2.F.7B
A8B2.F$F2.10B2A4B.F2.7B2AB2A4B.F2.7B2A3BA3B.F.6B2ABA6B2.F.9B2A5B2.F$F
2.8BA7B.F2.10B2A4B.F2.4BABA9B.F.4B3AB2A6B2.F.4BA3B2A6B2.F$F2.4B2ABA3B
A4B.F2.3B3AB2A2B2A3B.F2.3B2A4BA6B.F.4B2A10B2.F.3BA3B2ABA5B2.F$F2.3B2A
B2A3B2A3B.F2.3BA6B3A3B.F2.2BA2BA2BA7B.F.3BA2BA2B2A5B2.F.3BA2B3ABA5B2.
F$F2.4B4ABA6B.F2.3B2A4B3A4B.F2.3B2A3BA3BA3B.F.3B2ABAB3A5B2.F.3B2ABABA
BA5B2.F$F2.6BABABA5B.F2.8B2A6B.F2.3BABA2BA7B.F.4BABA9B2.F.16B2.F$F2.
4B2A10B.F2.4B2A3BA6B.F2.4BA11B.F.4B5A7B2.F.3B2A3BA7B2.F$F2.3BA5BA6B.F
2.3BA4B3A5B.F2.3BA2B2A8B.F.4BA2BA8B2.F.3B2A11B2.F$F2.4B4AB2A5B.F2.4B
3AB3A5B.F2.3B3A5BA4B.F.4BAB2A8B2.F.3B2AB3A7B2.F$F2.5BA5BA4B.F2.4BA3BA
2BA4B.F2.4BA6BA4B.F.4BA2BA3BA4B2.F.7B2ABA5B2.F$F2.6B2A3BA4B.F2.6B3A2B
A4B.F2.5B2AB2A6B.F.6BA2B2A2BA2B2.F.5B2AB3A5B2.F$F2.7BABAB2A3B.F2.6B2A
2B3A3B.F2.9B4A3B.F.6BABA2B2A3B2.F.6BABA2B2A3B2.F$F2.8BA7B.F2.5B4A7B.F
2.4BA3BA7B.F.5B2A2BA6B2.F.4BA11B2.F$F2.4B3A9B.F2.4B2A3B2A5B.F2.4B2ABA
2BA5B.F.4B3A9B2.F.4BABA2BA6B2.F$F2.4BA4B3A4B.F2.3BA5B2A5B.F2.3BA12B.F
.4BA4B3A4B2.F.3BA5BA2BA3B2.F$F2.4B3A2BA6B.F2.4B4ABA6B.F2.4B2ABAB2A5B.
F.4B3A3B3A3B2.F.3B2ABA2BA2BA3B2.F$F2.7B2A7B.F2.5BAB2A7B.F2.4BA5B2A4B.
F.4BA2BA8B2.F.4BA2BA8B2.F$F2.7BA3B2A3B.F2.6B3AB3A3B.F2.4B2A4B2A4B.F.
6BA3B3A3B2.F.3B2ABA4BA4B2.F$F2.4B2A4B2A4B.F2.3BABA2BABA5B.F2.2B2ABA2B
A7B.F.3B2ABABA7B2.F.3B2ABABAB2A4B2.F$F2.3B3ABABA2BA3B.F2.2B2ABA4B3A3B
.F2.3BA2B2A8B.F.4BA2B3A6B2.F.8BA2B2A3B2.F!

[amling]

I was looking at trying to extend work on minimum unstaggered height for 2c/5 even, mostly because it involved some new search ideas and seemed maybe just in range.

I started with this 2c5-s2s input file, describing all even centers using wildcards, "f.in":

Code: Select all

|  ..YYYYYYYYYYY... |  ..YYYYYYYYYYY... |  ..YYYYYYYYYYY... | ...YYYYYYYYYYY..  | ...YYYYYYYYYYY..  |
|  ..YYYYYYYYYYY... |  ..YYYYYYYYYYY... |  ..YYYYYYYYYYY... | ...YYYYYYYYYYY..  | ...YYYYYYYYYYY..  |

This of course includes the all-zeros center which is undesirable. We can split it on the "first" (as in left-most in this view) bit via...

Code: Select all

sed 's/Y/./' f.in > f0.in
sed 's/Y/*/' f.in > f1.in

...and get...

Code: Select all

|  ...YYYYYYYYYY... |  ..YYYYYYYYYYY... |  ..YYYYYYYYYYY... | ...YYYYYYYYYYY..  | ...YYYYYYYYYYY..  |
|  ...YYYYYYYYYY... |  ..YYYYYYYYYYY... |  ..YYYYYYYYYYY... | ...YYYYYYYYYYY..  | ...YYYYYYYYYYY..  |

Code: Select all

|  ..*YYYYYYYYYY... |  ..YYYYYYYYYYY... |  ..YYYYYYYYYYY... | ...YYYYYYYYYYY..  | ...YYYYYYYYYYY..  |
|  ..*YYYYYYYYYY... |  ..YYYYYYYYYYY... |  ..YYYYYYYYYYY... | ...YYYYYYYYYYY..  | ...YYYYYYYYYYY..  |

Repeating this we can split f0.in into f00.in and f01.in, etc. Then we delete the file which is "f000..000.in" with 55 zeros. Now some of these run to exhaustion and some don't. I gave it all 60 GB ulimit and repeated removing those that completed and splitting those that did not (automating with shell scripts to some degree). This eventually got down to the following fully-split but non-yet-exhausted input files:

Code: Select all

f0000000000000000000000000000000000000000000000000000001.in
f0000000000000010000000001100000000100100000011001100000.in
f0000000000000010000000001100000000100100000011001100001.in
f0000001000000000110000000010010000001100110000000000010.in
f0000001000000000110000000010010000001100110000000000011.in
f0000010000000000000000000000000000001000000000000000000.in
f0000010000000000000000000000000000001000000000000000001.in
f0000010010000001100110000000000010000010000000001100000.in
f0000010010000001100110000000000010000010000000001100001.in
f0000011000000001001000000110011000000000001000001000000.in
f0000011000000001001000000110011000000000001000001000001.in
f0000100000000000000000000010000000000000000000000000000.in
f0000100000000000000000000010000000000000000000000000001.in
f0000100000000011000000001001000000110011000000000000000.in
f0000100000000011000000001001000000110011000000000000001.in
f0000110011000000000001000001000000000110000000010010000.in
f0000110011000000000001000001000000000110000000010010001.in
f0001100000000100100000011001100000000000000000100000000.in
f0001100000000100100000011001100000000000000000100000001.in
f0010010000001100110000000000000000010000000001100000000.in
f0010010000001100110000000000000000010000000001100000001.in

I then opened it up and let each run with 1 TB ulimit. This exhausted all but:

Code: Select all

f0000010000000000000000000000000000001000000000000000000.in
f0000100000000000000000000010000000000000000000000000000.in

When I looked in the logs for these I found some problems, e.g. this:

Code: Select all

x = 101, y = 59, rule = LifeHistory
F2.7BA8B.F2.16B.F2.16B.F.6BA9B2.F.16B2.F$F2.7BA8B.F2.16B.F2.16B.F.6BA
9B2.F.16B2.F$F2.5B4A7B.F2.4B2AB2A7B.F2.4B3A9B.F.5B3A8B2.F.5B3A8B2.F$F
2.4B2A3BA6B.F2.4B2A10B.F2.3BABA10B.F.4BA11B2.F.3B2A3BA7B2.F$F2.3BA3BA
8B.F2.3BA3B2A7B.F2.3BABA2BA7B.F.3B2AB2ABA6B2.F.3BA2B3A7B2.F$F2.4B4A8B
.F2.4BA4BA6B.F2.3B2A2BABA6B.F.4B2A2BA2BA4B2.F.3B4AB2A6B2.F$F2.5B2AB3A
5B.F2.4BA3B2A6B.F2.8B3A5B.F.8BA7B2.F.8B2A6B2.F$F2.16B.F2.9BA6B.F2.8B
3A5B.F.9BA6B2.F.16B2.F$F2.16B.F2.11BA4B.F2.10B2A4B.F.16B2.F.16B2.F$F
2.10B3A3B.F2.10BABA3B.F2.10BABA3B.F.11BA4B2.F.10BA5B2.F$F2.10B3A3B.F
2.9BA2BA3B.F2.8B2A6B.F.9B2A5B2.F.9B3A4B2.F$F2.10BA5B.F2.7BAB2A5B.F2.
7BA8B.F.10BA5B2.F.16B2.F$F2.6B3A7B.F2.6BABAB2A4B.F2.5B4A7B.F.6BA3B2A
4B2.F.5B2A3BABA3B2.F$F2.5BAB2AB2A4B.F2.4B2A4B2A4B.F2.4BA2BAB3A4B.F.5B
2A4B2A3B2.F.4BAB2ABA6B2.F$F2.4B2ABA2BA5B.F2.4B2ABA8B.F2.3BA4BABA5B.F.
4B2A2B2AB2A3B2.F.4BA3B2A6B2.F$F2.5BABABABA4B.F2.4B2ABABA6B.F2.4BA2BA
8B.F.5B2ABA2BA4B2.F.4BABABA7B2.F$F2.6B2ABA6B.F2.6B2ABA6B.F2.5B3AB2A5B
.F.6BABAB2A4B2.F.5B2ABAB2A4B2.F$F2.9BABA4B.F2.9BA6B.F2.7BABA6B.F.8BA
7B2.F.8BA7B2.F$F2.9BABA4B.F2.8B2AB2A3B.F2.8B2A6B.F.8BA7B2.F.8B2A6B2.F
$F2.9BABA4B.F2.9BA6B.F2.8B3A5B.F.9BABA4B2.F.9B2A5B2.F$F2.10B3A3B.F2.
16B.F2.16B.F.10BA5B2.F.10BA5B2.F$F2.11B2A3B.F2.16B.F2.16B.F.16B2.F.
11BA4B2.F$F2.11BA4B.F2.11B2A3B.F2.10B2A4B.F.10BABA3B2.F.11BA4B2.F$F2.
9B2A5B.F2.9B2A5B.F2.9B3A4B.F.9BA2BA3B2.F.9BA6B2.F$F2.9BA6B.F2.9BA6B.F
2.8B2A6B.F.9B2A5B2.F.8B3A5B2.F$F2.11BA4B.F2.9BA6B.F2.16B.F.9BA6B2.F.
9B2A5B2.F$F2.9B2A5B.F2.8B3A5B.F2.7BA8B.F.16B2.F.8BA7B2.F$F2.8B2A6B.F
2.7B4A5B.F2.7BA2BA5B.F.7B2A7B2.F.7BA8B2.F$F2.6B2A8B.F2.6BA9B.F2.6BA9B
.F.6BA9B2.F.6BABA7B2.F$F2.6B2A8B.F2.5BA2BA7B.F2.5B3A8B.F.6BABA7B2.F.
5B2A9B2.F$F2.6B2A8B.F2.6BA9B.F2.6BA9B.F.6BA9B2.F.6BABA7B2.F$F2.8B2A6B
.F2.7B4A5B.F2.7BA2BA5B.F.7B2A7B2.F.7BA8B2.F$F2.9B2A5B.F2.8B3A5B.F2.7B
A8B.F.16B2.F.8BA7B2.F$F2.11BA4B.F2.9BA6B.F2.16B.F.9BA6B2.F.9B2A5B2.F$
F2.9BA6B.F2.9BA6B.F2.8B2A6B.F.9B2A5B2.F.8B3A5B2.F$F2.9B2A5B.F2.9B2A5B
.F2.9B3A4B.F.9BA2BA3B2.F.9BA6B2.F$F2.11BA4B.F2.11B2A3B.F2.10B2A4B.F.
10BABA3B2.F.11BA4B2.F$F2.11B2A3B.F2.16B.F2.16B.F.16B2.F.11BA4B2.F$F2.
10B3A3B.F2.16B.F2.16B.F.10BA5B2.F.10BA5B2.F$F2.9BABA4B.F2.9BA6B.F2.8B
3A5B.F.9BABA4B2.F.9B2A5B2.F$F2.9BABA4B.F2.8B2AB2A3B.F2.8B2A6B.F.8BA7B
2.F.8B2A6B2.F$F2.9BABA4B.F2.9BA6B.F2.7BABA6B.F.8BA7B2.F.8BA7B2.F$F2.
6B2ABA6B.F2.6B2ABA6B.F2.5B3AB2A5B.F.6BABAB2A4B2.F.5B2ABAB2A4B2.F$F2.
5BABABABA4B.F2.4B2ABABA6B.F2.4BA2BA8B.F.5B2ABA2BA4B2.F.4BABABA7B2.F$F
2.4B2ABA2BA5B.F2.4B2ABA8B.F2.3BA4BABA5B.F.4B2A2B2AB2A3B2.F.4BA3B2A6B
2.F$F2.5BAB2AB2A4B.F2.4B2A4B2A4B.F2.4BA2BAB3A4B.F.5B2A4B2A3B2.F.4BAB
2ABA6B2.F$F2.6B3A7B.F2.6BABAB2A4B.F2.5B4A7B.F.6BA3B2A4B2.F.5B2A3BABA
3B2.F$F2.10BA5B.F2.7BAB2A5B.F2.7BA8B.F.10BA5B2.F.16B2.F$F2.10B3A3B.F
2.9BA2BA3B.F2.8B2A6B.F.9B2A5B2.F.9B3A4B2.F$F2.10B3A3B.F2.10BABA3B.F2.
10BABA3B.F.11BA4B2.F.10BA5B2.F$F2.16B.F2.11BA4B.F2.10B2A4B.F.16B2.F.
16B2.F$F2.16B.F2.9BA6B.F2.8B3A5B.F.9BA6B2.F.16B2.F$F2.5B2AB3A5B.F2.4B
A3B2A6B.F2.8B3A5B.F.8BA7B2.F.8B2A6B2.F$F2.4B4A8B.F2.4BA4BA6B.F2.3B2A
2BABA6B.F.4B2A2BA2BA4B2.F.3B4AB2A6B2.F$F2.3BA3BA8B.F2.3BA3B2A7B.F2.3B
ABA2BA7B.F.3B2AB2ABA6B2.F.3BA2B3A7B2.F$F2.4B2A3BA6B.F2.4B2A10B.F2.3BA
BA10B.F.4BA11B2.F.3B2A3BA7B2.F$F2.5B4A7B.F2.4B2AB2A7B.F2.4B3A9B.F.5B
3A8B2.F.5B3A8B2.F$F2.7BA8B.F2.16B.F2.16B.F.6BA9B2.F.16B2.F$F2.7BA8B.F
2.16B.F2.16B.F.6BA9B2.F.16B2.F!

It has returned to the same 2 row slice and this of course can thus loop forever. I started doing rounds of noticing these in partials and ripping them out one at a time with forbid_grid (and restarting the searches), but then something magical happened:

Code: Select all

x = 101, y = 51, rule = LifeHistory
F2.6BA9B.F2.16B.F2.6BA9B.F.16B2.F.16B2.F$F2.6BA9B.F2.16B.F2.6BA9B.F.
16B2.F.16B2.F$F2.5B3A8B.F2.5B3A8B.F2.4B4A8B.F.4B2AB2A7B2.F.4B3A9B2.F$
F2.4BA11B.F2.3B2A3BA7B.F2.3B2A3BA7B.F.4B2A10B2.F.3BABA10B2.F$F2.3B2AB
2ABA6B.F2.3BA2B3A7B.F2.2BA3BA9B.F.3BA3B2A7B2.F.3BABA2BA7B2.F$F2.4B2A
2BA2BA4B.F2.3B4AB2A6B.F2.3B4A9B.F.4BA4BA6B2.F.3B2A2BABA6B2.F$F2.8BA7B
.F2.8B2A6B.F2.4B2AB3A6B.F.4BA3B2A6B2.F.8B3A5B2.F$F2.9BA6B.F2.16B.F2.
16B.F.9BA6B2.F.8B3A5B2.F$F2.16B.F2.16B.F2.16B.F.11BA4B2.F.10B2A4B2.F$
F2.11BA4B.F2.10BA5B.F2.9B3A4B.F.10BABA3B2.F.10BABA3B2.F$F2.9B2A5B.F2.
9B3A4B.F2.9B3A4B.F.9BA2BA3B2.F.8B2A6B2.F$F2.10BA5B.F2.16B.F2.9BA6B.F.
7BAB2A5B2.F.7BA8B2.F$F2.6BA3B2A4B.F2.5B2A3BABA3B.F2.5B3A8B.F.6BABAB2A
4B2.F.5B4A7B2.F$F2.5B2A4B2A3B.F2.4BAB2ABA6B.F2.4BAB2AB2A5B.F.4B2A4B2A
4B2.F.4BA2BAB3A4B2.F$F2.4B2A2B2AB2A3B.F2.4BA3B2A6B.F2.3B2ABA2BA6B.F.
4B2ABA8B2.F.3BA4BABA5B2.F$F2.5B2ABA2BA4B.F2.4BABABA7B.F2.4BABABABA5B.
F.4B2ABABA6B2.F.4BA2BA8B2.F$F2.6BABAB2A4B.F2.5B2ABAB2A4B.F2.5B2ABA7B.
F.6B2ABA6B2.F.5B3AB2A5B2.F$F2.8BA7B.F2.8BA7B.F2.8BABA5B.F.9BA6B2.F.7B
ABA6B2.F$F2.8BA7B.F2.8B2A6B.F2.8BABA5B.F.8B2AB2A3B2.F.8B2A6B2.F$F2.9B
ABA4B.F2.9B2A5B.F2.8BABA5B.F.9BA6B2.F.8B3A5B2.F$F2.10BA5B.F2.10BA5B.F
2.9B3A4B.F.16B2.F.16B2.F$F2.16B.F2.11BA4B.F2.10B2A4B.F.16B2.F.16B2.F$
F2.10BABA3B.F2.11BA4B.F2.10BA5B.F.11B2A3B2.F.10B2A4B2.F$F2.9BA2BA3B.F
2.9BA6B.F2.8B2A6B.F.9B2A5B2.F.9B3A4B2.F$F2.9B2A5B.F2.8B3A5B.F2.8BA7B.
F.9BA6B2.F.8B2A6B2.F$F2.9BA6B.F2.9B2A5B.F2.10BA5B.F.9BA6B2.F.16B2.F$F
2.16B.F2.8BA7B.F2.8B2A6B.F.8B3A5B2.F.7BA8B2.F$F2.7B2A7B.F2.7BA8B.F2.
7B2A7B.F.7B4A5B2.F.7BA2BA5B2.F$F2.6BA9B.F2.6BABA7B.F2.5B2A9B.F.6BA9B
2.F.6BA9B2.F$F2.6BABA7B.F2.5B2A9B.F2.5B2A9B.F.5BA2BA7B2.F.5B3A8B2.F$F
2.6BA3BA5B.F2.6BA9B.F2.5B2A9B.F.6BA2BA6B2.F.6BA2BA6B2.F$F2.7BA8B.F2.
7B2ABA5B.F2.7B3A6B.F.7B2ABA5B2.F.7B2ABA5B2.F$F2.8B3A5B.F2.9BA6B.F2.8B
2A6B.F.8BABA5B2.F.7B2A7B2.F$F2.5B4A7B.F2.4BA11B.F2.16B.F.16B2.F.16B2.
F$F2.4B5A7B.F2.4BA11B.F2.3B2A11B.F.4B2A10B2.F.3B4A9B2.F$F2.3BA4B3A5B.
F2.3BA6BA5B.F2.3BABA3BA6B.F.3B2AB2A8B2.F.3BA3B2A7B2.F$F2.4B2AB2A2BA4B
.F2.4B2AB2ABA5B.F2.3BAB2A2BA6B.F.4BAB2AB2A5B2.F.3B2A2BAB2A5B2.F$F2.5B
2A9B.F2.4B2A10B.F2.4BA3BA7B.F.5BA3BA6B2.F.5BA3B2A5B2.F$F2.7B2A7B.F2.
6B2A8B.F2.5B3A8B.F.6B3A7B2.F.6B4A6B2.F$F2.11BA4B.F2.8BABA5B.F2.7BABA
6B.F.8BA2BA4B2.F.8B2A6B2.F$F2.9BABA4B.F2.10BA5B.F2.9BABA4B.F.10BA5B2.
F.10BA5B2.F$F2.16B.F2.12BA3B.F2.9BA6B.F.9B2ABA3B2.F.9B2A5B2.F$F2.10B
3A3B.F2.9B3A4B.F2.9B3A4B.F.9BA2BA3B2.F.9B2AB2A2B2.F$F2.9B2A5B.F2.8BA
7B.F2.9B2A5B.F.12BA3B2.F.16B2.F$F2.8B2A6B.F2.16B.F2.8B2A6B.F.8BA7B2.F
.7B2A7B2.F$F2.7BABA6B.F2.7BAB2A5B.F2.6B2AB2A5B.F.7B2A2BA4B2.F.7B2A7B
2.F$F2.7BABA6B.F2.6B2AB2A5B.F2.6BA3BA5B.F.6BA4BA4B2.F.6BA4BA4B2.F$F2.
7B2A2B2A3B.F2.7B2A7B.F2.6B4A6B.F.7B4A5B2.F.7BA2BA5B2.F$F2.16B.F2.16B.
F2.16B.F.8B2A6B2.F.7BA2BA5B2.F$F2.16B.F2.16B.F2.16B.F.16B2.F.16B2.F$F
2.16B.F2.16B.F2.16B.F.16B2.F.16B2.F!

That is the shortest (in search depth) result between the two log files. There are others and of course if I include all the various cycles with symmetric parts there is a complex grammar of them.

In life history with the envelope filled in as dark blue state:

Code: Select all

x = 96, y = 11, rule = LifeHistory
96B$13BA30BA6BA30BA13B$12BABA19BA8B3A4B3A8BA19BABA12B$11B2AB2A17B3A7B
A2BA2BA2BA7B3A17B2AB2A11B$11BA2B2A2B3A11B2AB2A7BAB4ABA7B2AB2A11B3A2B
2A2BA11B$B3A6BABAB2ABA3BA22BABA2BABA22BA3BAB2ABABA6B3AB$BA2BA5BAB5A2B
ABA8B5A7B2A8B2A7B5A8BABA2B5ABA5BA2BAB$2B4A2BA4BA2BA6B3A3BA4BA3BA2BA2B
A6BA2BA2BA3BA4BA3B3A6BA2BA4BA2B4A2B$5B2A6BA2BABA5BABABA3BA3B3A18B3A3B
A3BABABA5BABA2BA6B2A5B$BA4BAB2A2BA16BA2B5A2BA3BA8BA3BA2B5A2BA16BA2B2A
BA4BAB$BA4BA18B2A7B2A24B2A7B2A18BA4BAB!

I had considered trying to automate some of this wildcard splitting as a more general feature, but haven't come up with anything I particularly like. It's hard to programmatically detect/manage processes that hit ulimit and die and so automating "from outside" is tough, but automating "from inside" the search process (as my first sketch does) is going to be particularly messy to checkpoint or interpret orchestration state and is not so straight-forward to do hacks with like how I excluded "f000...000.in" here.

[Sokwe]

I was looking at trying to extend work on minimum unstaggered height for 2c/5 even, mostly because it involved some new search ideas and seemed maybe just in range.... then something magical happened:...

Code: Select all

x = 96, y = 11, rule = LifeHistory
96B$13BA30BA6BA30BA13B$12BABA19BA8B3A4B3A8BA19BABA12B$11B2AB2A17B3A7B
A2BA2BA2BA7B3A17B2AB2A11B$11BA2B2A2B3A11B2AB2A7BAB4ABA7B2AB2A11B3A2B
2A2BA11B$B3A6BABAB2ABA3BA22BABA2BABA22BA3BAB2ABABA6B3AB$BA2BA5BAB5A2B
ABA8B5A7B2A8B2A7B5A8BABA2B5ABA5BA2BAB$2B4A2BA4BA2BA6B3A3BA4BA3BA2BA2B
A6BA2BA2BA3BA4BA3B3A6BA2BA4BA2B4A2B$5B2A6BA2BABA5BABABA3BA3B3A18B3A3B
A3BABABA5BABA2BA6B2A5B$BA4BAB2A2BA16BA2B5A2BA3BA8BA3BA2B5A2BA16BA2B2A
BA4BAB$BA4BA18B2A7B2A24B2A7B2A18BA4BAB!

Excellent! I was actually starting to doubt that such a ship existed. A similar project might be to find a "pure" (1,0)c/4 odd-symmetric height-9 spaceship ("pure" in this case meaning that it is not also gutter symmetric).

I also don't know if there are any (2,0)c/4 odd-symmetric height-8 spaceships that are not also gutter symmetric (height-9 examples are known). Unfortunately, searching for such a ship is difficult, because starting from the edge gives endless combinations of XWSSs, while starting from the middle gives endless combinations of p2 components. I likewise don't know if there are any strict (2,0)c/4 height-8 even-width glide-symmetric spaceships (a height-9 example is known).

I also added a new table for minimum single-phase heights to the spaceship search status page (see the bottom of this section).

With some effort using WLS 0.63, I believe I should be able to confirm that all (2,0)c/4 single-phase height-6 spaceships are just combinations of interacting LWSSs and MWSSs, as well as this ship:

Code: Select all

x = 23, y = 6, rule = B3/S23
7b3o3b3o$bo4bo2bo3bo2bo4bo$3o3bo3bobo3bo3b3o$ob2obo2bobobobo2bob2obo$b
8o5b8o$b2o3b4o3b4o3b2o!

I haven't run the search yet, as it requires a fair amount of human attention, but if true, this would confirm that the minimum single-phase height for even-symmetric and "pure" odd-symmetric ships is 7. However, I don't know of a single-phase height-7 even-width glide-symmetric (2,0)c/4 ship (a height-8 example is known).

Assuming that there is just one (1,0)c/4 single-phase height-7 spaceship, I would probably be able to confirm this with WLS 0.63. A single-phase height-8 gutter-symmetric ship is known, but I don't know of any height-8 even-symmetric or "pure" odd-symmetric ships for this speed.

The final unknown up to period 5 in this new table is the potential existence of a (2,0)c/5 single-phase height-9 even-symmetric spaceship (your new 2c/5 ship quoted above is height-10). I'm not sure how difficult any of these searches would be to set up or run with LLSSS, but I thought I'd throw the idea out there.

[amling]

Many of these are approachable with some combination of wildcard init, grid_loop constraint and forbid_grid filter. I'll post them as I complete them and hope that this transgression against the no-adjacent-posts convention is forgivable on a back alley thread like this.

I looked first at c/4 odd-but-not-gutter. 4 is low enough that odd wildcard init is merely a little slow (and perhaps underoptimized as it's not something I do super often) and so we can do something like...

Code: Select all

$ cat n1.H36.in
| ..YYYYYYYYY.. | ..YYYYYYYYY.. | ..YYYYYYYYY.. | ..YYYYYYYYY.. |
| ..WWWWWWWWW.. | ..WWWWWWWWW.. | ..WWWWWWWWW.. | ..WWWWWWWWW.. |
| ..YYYYYYYYY.. | ..YYYYYYYYY.. | ..YYYYYYYYY.. | ..YYYYYYYYY.. |

Then to forbid a globally-gutter pattern we'll use forbid_grid filter with:

Code: Select all

$ cat n1.H36.bad
| WWWWWWWWWWWWW | WWWWWWWWWWWWW | WWWWWWWWWWWWW | WWWWWWWWWWWWW |
| ............. | ............. | ............. | ............. |
| WWWWWWWWWWWWW | WWWWWWWWWWWWW | WWWWWWWWWWWWW | WWWWWWWWWWWWW |

This is a multiple of 4 so no grid_loop constraint needed and completes on my laptop in ~5m and a very small amount of memory (VmPeak 4.55 GB but much of that is overhead like thread stacks and the binary itself). This was run as:

Code: Select all

$ rlife llsss c4-s2s n1.H36.in --filters forbid_grid:n1.H36.bad

The longest partial was:

Code: Select all

x = 65, y = 72, rule = LifeHistory
F.4BA8B.F.3B2ABA6B.F.3BA2BA6B.F.6B2A5B.F$F.6BA2BA3B.F.5BA7B.F.6BA6B.F
.5B3A5B.F$F.4BA8B.F.3B2ABA6B.F.3BA2BA6B.F.6B2A5B.F$F.3B4A6B.F.3B3A7B.
F.2BA2B2A6B.F.2B5A6B.F$F.13B.F.3BA3BA5B.F.3BA3B2A4B.F.3BA3BA5B.F$F.4B
AB2A5B.F.5B4A4B.F.4B2A7B.F.3B3A7B.F$F.4BA2B2A4B.F.4BA2B2A4B.F.4BA8B.F
.4BABA6B.F$F.5BA3BA3B.F.5B5A3B.F.5B2A2BA3B.F.5B2ABA4B.F$F.6BA3BA2B.F.
13B.F.6B3A4B.F.5B4A4B.F$F.13B.F.13B.F.13B.F.7B2A4B.F$F.13B.F.13B.F.9B
A3B.F.8B2A3B.F$F.8B2A3B.F.8B3A2B.F.7B2ABA2B.F.7B2ABA2B.F$F.7BAB2A2B.F
.6B2AB2A2B.F.6BA3BA2B.F.6BA6B.F$F.6B2A5B.F.6B2A5B.F.6B3A4B.F.5BA2BA4B
.F$F.7BA5B.F.13B.F.6B2A5B.F.6BABA4B.F$F.5BAB2A4B.F.5BA2BA4B.F.13B.F.
5B2A6B.F$F.5B3A5B.F.4BA3BA4B.F.4B2A7B.F.4B2A7B.F$F.5B2A6B.F.4BA8B.F.
4B2A7B.F.3BA9B.F$F.5BABA5B.F.5BABA5B.F.4B3A6B.F.6BA6B.F$F.6B2A5B.F.5B
A7B.F.5BA7B.F.4B3A6B.F$F.6B4A3B.F.6BA2BA3B.F.13B.F.13B.F$F.8BABA2B.F.
10BA2B.F.7B2ABA2B.F.7B3A3B.F$F.8BABA2B.F.7B2ABA2B.F.7BA2BA2B.F.7B3A3B
.F$F.8B2A3B.F.7B3A3B.F.13B.F.13B.F$F.6BA6B.F.5B2ABA4B.F.5BA3BA3B.F.6B
A6B.F$F.5B3A5B.F.5B3A5B.F.5BABA5B.F.4B2A7B.F$F.13B.F.13B.F.5BA7B.F.5B
A7B.F$F.5B3A5B.F.6B2A5B.F.6BA6B.F.5B2A6B.F$F.8BA4B.F.5BA3BA3B.F.5BA2B
A4B.F.5BA7B.F$F.4BA2B3A3B.F.4BAB2A2BA2B.F.4BAB2A5B.F.3B2AB2A5B.F$F.4B
3A2B2A2B.F.4BABA6B.F.3B2A3B3A2B.F.3B2A3B2A3B.F$F.6BA2B2A2B.F.4BAB2AB
2A2B.F.4BA3BA4B.F.8BA4B.F$F.4BABA6B.F.5B3A5B.F.4B2A7B.F.3B3A7B.F$F.7B
A5B.F.3BA3BA5B.F.3BA9B.F.3BABA7B.F$F.3B3ABA5B.F.3B3AB2A4B.F.2BA2BA7B.
F.2B3ABA6B.F$F.4BABABABA2B.F.3B2AB2ABA3B.F.3BA2B2ABA3B.F.6BA6B.F$F.
10BA2B.F.10BA2B.F.13B.F.8B3A2B.F$F.9BA3B.F.13B.F.9B2A2B.F.13B.F$F.13B
.F.9B2A2B.F.13B.F.8BA4B.F$F.6BA2B2A2B.F.6B2A5B.F.6BAB3A2B.F.9BA3B.F$F
.6B2A5B.F.5BA3BA3B.F.5BA7B.F.4B3A2BA3B.F$F.5BAB2A4B.F.5BA7B.F.4B2A7B.
F.6BA6B.F$F.6B3A4B.F.4BA4BA3B.F.4B2A7B.F.3BA2BA6B.F$F.4B5A4B.F.4BA8B.
F.4B2A7B.F.6BA6B.F$F.4BA2B3A3B.F.3B2A4BA3B.F.2BAB2A7B.F.3B2A2BA5B.F$F
.3BA2BA6B.F.2B2A2BA2BA3B.F.6B3A4B.F.2BA4B2A4B.F$F.2B2AB2A2BA3B.F.2B2A
B3A5B.F.2B2ABABA5B.F.2B4AB2A4B.F$F.3BA4BA4B.F.5BA7B.F.2BA2BA7B.F.2BA
2B2A6B.F$F.3B2A8B.F.3B2A8B.F.4BA8B.F.3B3A7B.F$F.4BA3BA4B.F.13B.F.3BAB
A7B.F.3BA2BA6B.F$F.4B2A3BA3B.F.4B2A7B.F.4B3A6B.F.4B4A5B.F$F.5BA7B.F.
4B2AB2A4B.F.7B2A4B.F.4BA2B2A4B.F$F.6B3A4B.F.5BAB2A4B.F.5BA3BA3B.F.7BA
BA3B.F$F.5BABA5B.F.5BA2BA4B.F.8BA4B.F.4BABA6B.F$F.5B2A6B.F.4B3A6B.F.
4B3A6B.F.4B2A7B.F$F.3BA9B.F.3BA9B.F.3BA9B.F.2B2A9B.F$F.3B6A4B.F.3B6A
4B.F.2B2AB4A4B.F.2B2AB3A5B.F$F.9BA3B.F.3BA5BA3B.F.3BA2BA3BA2B.F.6BABA
4B.F$F.3BAB2AB2A3B.F.4BA3B3A2B.F.3B2A3BABA2B.F.2B4ABABA3B.F$F.3BA5BA
3B.F.3BA5BA3B.F.3BA2BA6B.F.2B2A2BA6B.F$F.4B5A4B.F.3B7A3B.F.2BA2B3A5B.
F.5B3A5B.F$F.4BA4BA3B.F.3B2A4B2A2B.F.9B2A2B.F.4BA3BA4B.F$F.4BAB2AB2A
2B.F.4BAB2A5B.F.4B4A5B.F.3B4ABA4B.F$F.3B2AB2AB2A2B.F.3BA3BAB2A2B.F.3B
2A4B2A2B.F.3BA3B2A4B.F$F.3BABA7B.F.2BA2B5A3B.F.2BA2BABA5B.F.2BA5BA4B.
F$F.3B2A3BA4B.F.3B3A3BA3B.F.3BA5B2A2B.F.2B3A3B2A3B.F$F.6BA2B2A2B.F.4B
3A2BA3B.F.3BA4BA4B.F.8B2A3B.F$F.5BAB2A4B.F.5BABA5B.F.7BA5B.F.4B2A7B.F
$F.4BA2BAB2A2B.F.4BAB2ABA3B.F.4B5A4B.F.4B3AB2A3B.F$F.3BA9B.F.3BA6BA2B
.F.3BA4BABA2B.F.3BA2BABABA2B.F$F.4B6A3B.F.2BA6B2A2B.F.2BABA4B2A2B.F.
2B4AB2A4B.F$F.2B3AB2AB2A2B.F.3B2A8B.F15.F15.F!

For one more height step (9.25) we need a bigger input and then a constraint:

Code: Select all

$ cat n1.H40.in
| ..YYYYYYYYYY..  | ..YYYYYYYYYY..  | ..YYYYYYYYYY..  | ..YYYYYYYYYY..  |
| ..WWWWWWWWWW..  | ..WWWWWWWWWW..  | ..WWWWWWWWWW..  | ..WWWWWWWWWW..  |
| ..YYYYYYYYYY..  | ..YYYYYYYYYY..  | ..YYYYYYYYYY..  | ..YYYYYYYYYY..  |
$ cat n1.H40.bad
| WWWWWWWWWWWWWW  | WWWWWWWWWWWWWW  | WWWWWWWWWWWWWW  | WWWWWWWWWWWWWW  |
| ..............  | ..............  | ..............  | ..............  |
| WWWWWWWWWWWWWW  | WWWWWWWWWWWWWW  | WWWWWWWWWWWWWW  | WWWWWWWWWWWWWW  |
$ cat n1.H37.cstr
| ..WWWWWWWWWW.. | ..WWWWWWWWW... | ..WWWWWWWWW... | ..WWWWWWWWW... |

Constraints are applied to input grids (relevant mostly for wildcard expansion) and so we can use this overly large "H40" input just fine.

This is run as:

Code: Select all

$ rlife llsss c4-s2s n1.H40.in --constraint grid_loop:n1.H37.cstr --filters forbid_grid:n1.H40.bad

After about 10m with VmPeak at 6.58 GB this found this (height 10 bounding box shown, although I would call this height 9.25):

Code: Select all

x = 77, y = 10, rule = LifeHistory
23BA9BA9BA9BA23B$4BA17BABA7BA2BA2BA2BA2BA7BABA17BA4B$2B4A14B2A5B2A2BA
3B3AB3A3BA2B2A5B2A14B4A2B$B2A2BA9B3ABABABA3BAB3A5BABA5B3ABA3BABABAB3A
9BA2B2AB$A2B4A3B4A5BABA5BABA3BA2B2AB2A2BA3BABA5BABA5B4A3B4A2BA$A4B3AB
4A5BA6BAB2A2B3A9B3A2B2ABA6BA5B4AB3A4BA$5BA3BABA4B2A2B2A2B4ABA2BA2BABA
BABA2BA2BAB4A2B2A2B2A4BABA3BA5B$3A3BAB2A16B4A4BA2BABA2BA4B4A16B2ABA3B
3A$7BA4B2A10BA12BABA12BA10B2A4BA7B$24BA27BA24B!

I killed the search shortly after this as I have no way of preventing it from recombining this in endless useless variations with separate ships.

For explicitness, barring bugs this verifies the minimum odd-but-not-gutter c/4 ship height is 9.25.

[amling]

Next I took a look at c/4 even single-phase heights. This is the same sort of tricks, just with a somewhat different constraint.

Files:

Code: Select all

$ cat n2.H08.in
| ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. |
| ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. |
$ cat n2.H08.bad
| .................. | .................. | .................. | .................. |
| .................. | .................. | .................. | .................. |
$ cat n2.H08a.cstr
| .....WWWWWWWW..... | ....WWWWWWWWWW.... | ...WWWWWWWWWWWW... | ..WWWWWWWWWWWWWW.. |

The constraint has an extra "a" as I had tried all 4 phases (a, b, c, d) at height 7 and this one did the best. Arguably only the one generation needs to be restricted to get the right space of findable finite ships, but constraining all generations ahead of time (i.e. before the next row's constraint is realized) can eliminate some unnecessary search state in between.

This ran as:

Code: Select all

$ rlife llsss c4-s2s n2.H08.in --constraint grid_loop:n2.H08a.cstr --filters forbid_grid:n2.H08.bad

It took about 4m on my laptop (VmPeak 4.94 GB) with longest partial:

Code: Select all

x = 85, y = 81, rule = LifeHistory
F.10BA7B.F.10BA7B.F.11BA6B.F.10B2A6B.F$F.10BA7B.F.10BA7B.F.11BA6B.F.
10B2A6B.F$F.8BAB3A5B.F.7BA4BA5B.F.6B2A2BA7B.F.6BA3BA7B.F$F.6B2A2B3A5B
.F.6B5ABA5B.F.6B5ABA5B.F.6BABA9B.F$F.7BA10B.F.11BA6B.F.10B2A6B.F.6BA
3B2A6B.F$F.7B2A9B.F.6B3A9B.F.7BA10B.F.7BA10B.F$F.7BA10B.F.18B.F.6BABA
9B.F.7BA10B.F$F.5B3A10B.F.5BA2BA9B.F.18B.F.5BA12B.F$F.5B3A10B.F.4BA
13B.F.4B2A12B.F.4B2A12B.F$F.5B2A11B.F.4BA13B.F.4B2A12B.F.3BA2BA11B.F$
F.5BA2BA9B.F.5BA2BA9B.F.4B2A12B.F.18B.F$F.6B2ABA8B.F.5BA3BA8B.F.5B3AB
A8B.F.4B4ABA8B.F$F.6B3ABA7B.F.6BAB2A8B.F.8B2A8B.F.9BA8B.F$F.18B.F.18B
.F.7BA10B.F.8BA9B.F$F.8B2A8B.F.8B2A8B.F.18B.F.18B.F$F.8B2A8B.F.18B.F.
8BA9B.F.7B2A9B.F$F.7B2A9B.F.7BA10B.F.7B2A9B.F.7BABA8B.F$F.8BA9B.F.7B
2A9B.F.7BABA8B.F.7BA10B.F$F.18B.F.8B2A8B.F.18B.F.8BA9B.F$F.8B2A8B.F.
8B2A8B.F.7BA10B.F.18B.F$F.8B2A8B.F.8B3A7B.F.7BA2BA7B.F.7B2A9B.F$F.11B
A6B.F.8B2A8B.F.8BA9B.F.8B3A7B.F$F.8BA3BA5B.F.11BA6B.F.9BABA6B.F.8B2A
8B.F$F.7BA2BA7B.F.6BA3B2A6B.F.9BABA6B.F.6BA2BAB2A5B.F$F.6B4ABA6B.F.6B
A2B2A7B.F.5B3ABABA6B.F.6B2ABA8B.F$F.7B2A9B.F.6BA2BA8B.F.8B2A8B.F.6BA
11B.F$F.18B.F.9BA8B.F.8B2A8B.F.18B.F$F.7B2AB2A6B.F.7BA2B2A6B.F.9BABA
6B.F.7BAB2A7B.F$F.6BA4BA6B.F.6BA3B2A6B.F.6B2A10B.F.6B3ABA7B.F$F.6BA
11B.F.6BA2B2A7B.F.6BABA2BA6B.F.5B2ABA9B.F$F.5B2AB3A7B.F.5B2AB2A8B.F.
5BA2BA9B.F.5BA2B2A8B.F$F.7B2A9B.F.6B2A2BA7B.F.5B3A2BA7B.F.5BA12B.F$F.
9BA8B.F.9BA8B.F.7B3A8B.F.7B3A8B.F$F.7B2A9B.F.8BA9B.F.18B.F.18B.F$F.
18B.F.6BA11B.F.5B3A10B.F.5BABA10B.F$F.5B2AB3A7B.F.5B2A3BA7B.F.5B2A11B
.F.4BA3BA9B.F$F.6B5A7B.F.5BA4BA7B.F.5BABAB2A7B.F.5BABAB2A7B.F$F.7BA
10B.F.6B2ABA8B.F.6BA3BA7B.F.6BA11B.F$F.18B.F.11BA6B.F.10B2A6B.F.18B.F
$F.10B3A5B.F.10BABA5B.F.9B2ABA5B.F.9B2ABA5B.F$F.10BABA5B.F.9B2ABA5B.F
.12BA5B.F.9BABA6B.F$F.9BA8B.F.9B3A6B.F.8BA9B.F.18B.F$F.8BABA7B.F.9B2A
7B.F.8BA9B.F.7B2A9B.F$F.11BA6B.F.9BABA6B.F.8B2ABA6B.F.7B3A8B.F$F.7BA
2B2A6B.F.6B2A2B2A6B.F.6BA5BA5B.F.8B2AB2A5B.F$F.6B2A2BA7B.F.6B6A6B.F.
5BA3BABA6B.F.5B2A11B.F$F.6BA2BA8B.F.6B2A10B.F.6BA11B.F.6B3A9B.F$F.18B
.F.8B2A8B.F.7B2A9B.F.7B2A9B.F$F.8B2A8B.F.18B.F.9BA8B.F.7BA10B.F$F.18B
.F.7BABA8B.F.7BA10B.F.18B.F$F.7B2A9B.F.7B2A9B.F.7BABA8B.F.7BA10B.F$F.
7BABA8B.F.9BA8B.F.6B2A10B.F.6B2A10B.F$F.6B2ABA8B.F.5BABA10B.F.8BA9B.F
.6BABA9B.F$F.5B2A11B.F.8BA9B.F.5BA2BA9B.F.5BA2BA9B.F$F.5B2ABA2BA6B.F.
5B3A3B2A5B.F.5B3A3B2A5B.F.4B2AB3ABA6B.F$F.11B2A5B.F.5BA5B2A5B.F.5BA2B
ABA7B.F.5BA2BABA7B.F$F.6B2A4BA5B.F.6B3ABAB2A4B.F.6B3ABA7B.F.5B2ABABA
7B.F$F.6B2AB2ABA5B.F.9B2AB2A4B.F.6BA2B2AB2A4B.F.6BA5BA5B.F$F.7BAB2ABA
5B.F.7BA10B.F.8BAB2A6B.F.7B2A3BA5B.F$F.7BA2BA7B.F.8BABA7B.F.8BABA7B.F
.7B2ABA7B.F$F.10BA7B.F.9B2A7B.F.8BABA7B.F.7BA10B.F$F.6BA2BA8B.F.8BA9B
.F.6BA11B.F.5B2ABA9B.F$F.5BA2B3A7B.F.5B6A7B.F.5B2AB2A8B.F.5B3ABA8B.F$
F.6BA4BA6B.F.6BA11B.F.5BA4BA7B.F.5BA4BA7B.F$F.7B3A8B.F.7B3A8B.F.6B4A
8B.F.6B5A7B.F$F.8BA3BA5B.F.7BA2BA7B.F.7BA2BA7B.F.10B2A6B.F$F.9B2A7B.F
.10BA7B.F.7BA2B2A6B.F.9BA8B.F$F.6B3ABABA5B.F.6BABABA7B.F.10B2A6B.F.6B
2AB3A6B.F$F.6B2A4BA5B.F.5BA4BA7B.F.5B2ABA9B.F.5B2ABA2BA6B.F$F.5BA3B2A
7B.F.6BAB4A6B.F.5B2AB2ABA6B.F.4BA3B2A8B.F$F.9BABA6B.F.6B2A3BA6B.F.5B
2ABA3BA5B.F.4BA3BA3BA5B.F$F.6B3AB2A6B.F.6BA3B2A6B.F.5B2A3B2A6B.F.9BAB
A6B.F$F.7B2A9B.F.6BABA9B.F.6BABA9B.F.5B3ABA8B.F$F.10B2A6B.F.7B5A6B.F.
10B2A6B.F.7BA3BA6B.F$F.7BA2B2A6B.F.6B2ABA2BA5B.F.6BA5BA5B.F.7B3A2BA5B
.F$F.6B2A2B2A6B.F.7B2ABABA5B.F.7B3ABA6B.F.6BAB2A8B.F$F.5BABA4BA5B.F.
5BA12B.F.6BABA9B.F.5B2A4BA6B.F$F.5B2AB3A7B.F.5BA3B3A6B.F.4B2A2B4A6B.F
.4B2A2B4A6B.F$F.7B2A2BA6B.F.5BAB2A2BA6B.F.5BABA4BA5B.F.7BA2BAB2A4B.F$
F.5BA5BA6B.F.6BAB4A6B.F.5B2ABA3BABA3B.F.7BA4B4A2B.F$F.6BABABA7B.F20.F
20.F20.F!

Height 9 is known to exist, e.g. this height 10 ship linked in the all-phases table for c/4 even has two height 9 phases:

Code: Select all

x = 80, y = 29, rule = LifeHistory
30B4A12B4A30B$3B3A17B2A3B2AB3A3BA4BA3B3AB2A3B2A17B3A3B$B2A2BA17BABA2B
3AB6A4B6AB3A2BABA17BA2B2AB$A2B2A20B2AB2A5BA2BA2BA2BA5B2AB2A20B2A2BA$
3A3B2ABA11BA7BA20BA7BA11BAB2A3B3A$B2A3B2AB2A7B4A6BA8B6A8BA6B4A7B2AB2A
3B2AB$2A4BA2BABAB2A4BABA2B2A11B2A2B2A11B2A2BABA4B2ABABA2BA4B2A$14B4A
6B2A11B2A2B2A11B2A6B4A14B$10B2A2B2A48B2A2B2A10B12$30B3A14B3A30B$4B2A
23B4A14B4A23B2A4B$B2A2BA17B3A3BA4BA2B2A2B2A2BA4BA3B3A17BA2B2AB$BA21BA
11BAB2A2B2ABA11BA21BAB$AB2A3BA16BA2B2A5BA2BA4BA2BA5B2A2BA16BA3B2ABA$
7B4A7B2AB2A2BAB2A8BA4BA8B2ABA2B2AB2A7B4A7B$A4BA11BABAB2A13B3A2B3A13B
2ABABA11BA4BA$BA4B5AB2AB3ABAB5A10BA2B2A2BA10B5ABAB3AB2AB5A4BAB$BA5B2A
3BABAB2A6B2A11BA4BA11B2A6B2ABABA3B2A5BAB!

I ran the H09a search anyway which took ~22m (VmPeak 21.46 GB) to find first this little one (one height 9 phase but also one height 11 phase), after which I killed it immediately:

Code: Select all

x = 36, y = 9, rule = B3/S23
5b3obo16bob3o$4b3o2b2o14b2o2b3o$3b3o3b3o3bo4bo3b3o3b3o$2bo6b7o4b7o6bo$
4bo3b2o3bo2bo2bo2bo3b2o3bo$b2ob2o24b2ob2o$bo13b6o13bo$15b2o2b2o$2o13b
2o2b2o13b2o!

For explicitness, barring bugs this verifies the minimum even c/4 single-phase ship height to be 9.

[amling]

Next c/4 odd-but-not-gutter single-phase height which went down very similarly to c/4 even single-phase, but with slower state init due to odd wildcards.

I tried all four phases for height 7 (exhausted) and just like with even, "a" did best.

Files:

Code: Select all

$ cat n2.H08.in
| ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. |
| ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. | ..YYYYYYYYYYYYYY.. |
$ cat n2.H08.bad
| .................. | .................. | .................. | .................. |
| .................. | .................. | .................. | .................. |
$ cat n2.H08a.cstr
| .....WWWWWWWW..... | ....WWWWWWWWWW.... | ...WWWWWWWWWWWW... | ..WWWWWWWWWWWWWW.. |

This ran as:

Code: Select all

$ rlife llsss c4-s2s n3.H08.in --constraint grid_loop:n3.H08a.cstr --filters forbid_grid:n3.H08.bad

It took ~8m on my laptop (VmPeak 5.83 GB) to first find this:

Code: Select all

x = 77, y = 8, rule = B3/S23
22b3o7b3o3bo3b3o7b3o$3b3o14bo2b2o2b2o3b4obobob4o3b2o2b2o2bo14b3o$b2o2b
o10b2obobob5obobo5bobo5bobob5obobob2o10bo2b2o$o2b2o10b2ob2obo3bo3bo2b
2o3bobo3b2o2bo3bo3bob2ob2o10b2o2bo$3o3b2ob10o2b3obo2bobob2o3bobo3b2obo
bo2bob3o2b10ob2o3b3o$b2o3b2obo3b2o5b2o3b2obo19bob2o3b2o5b2o3bob2o3b2o$
2o4b3o4bo19b5ob5o19bo4b3o4b2o$10bob2o9b3o2b2o5b2o3b2o5b2o2b3o9b2obo!

For explicitness, barring bugs this verifies the minimum odd-but-not-gutter c/4 single-phase ship height to be 8.

[amling]

Next I took a look at unstaggered 2c/4 odd-but-not-gutter.

I agree that from a true exhaustion perspective both the sides and the center are both unappealing to start from. Maybe the center start could be divied up according to whether or not the center 3 rows (with symmetry) are strict c/2 or not? If they're not then there is an easy LLSSS setup to find them (forbid 3 rows of strict c/2), but if they are it's a bigger problem. You'd have to produce a closed list of all 2 row boundaries reachable from an odd-but-not-gutter c/2 start, and then starting from each of them (or the union) force the third row to not be strict c/2. I suspect this would be well in range in terms of today's computer power but it would be a fair bit of custom code (although maybe some of the support code is written between the various "proj" stuff and slices-tool both doing a bunch of juggling collections of slices).

Another possibility is to set up the non-strict-2c/4 search for an odd-by-not-gutter 2c/4 ship and add a forbid_grid filter forcing it to not still be completely c/2 by some search fix depth D. Each such fixed D search is not exhaustive but their (infinite) union is.

I ran the height 8 D=30 version of this hoping to get lucky...

Code: Select all

$ cat n4.H08.in
|  ..YYYYYYYY... |  ..YYYYYYYY... | ...YYYYYYYY..  | ...YYYYYYYY..  |
|  ..WWWWWWWW... |  ..WWWWWWWW... | ...WWWWWWWW..  | ...WWWWWWWW..  |
|  ..YYYYYYYY... |  ..YYYYYYYY... | ...YYYYYYYY..  | ...YYYYYYYY..  |
$ cat n4.H08.cstr
|  ..WWWWWWWW... |  ..WWWWWWWW... | ...WWWWWWWW..  | ...WWWWWWWW..  |
$ cat n4.H08.bad
|  WWWWWWWWWWWWW |  WWWWWWWWWWWWW | WWWWWWWWWWWWW  | WWWWWWWWWWWWW  |
|  ............. |  ............. | .............  | .............  |
|  WWWWWWWWWWWWW |  WWWWWWWWWWWWW | WWWWWWWWWWWWW  | WWWWWWWWWWWWW  |
$ uniq -c n4.H08-D30.bad2
     30 |  2222222222222 |  2222222222222 | 2222222222222  | 2222222222222  |
$ rlife llsss 2c4-s2s n4.H08.in --constraint grid_loop:n4.H08.cstr --filters forbid_grid:n4.H08.bad,forbid_grid:n4.H08-D30.bad2
...

...and it ends up exactly like you'd expect (longest partial): 29 rows of strict c/2 crud followed by ~20 rows of 2c/4 partial. I'm probably not going to push this as my money is on no result existing (it would have to be dozens of rows of pure c/2 around the pure c/2 center that then somehow connected to a 2c/4 outer completion).

Unstaggered 2c/4 gse-but-not-even seems even worse for techniques known to me due to things like this:

Code: Select all

|  ........... |  ......*.... | ...........  | ...........  |
|  ........... |  ........... | ...........  | ......*....  |
|  ........... |  ........... | .....***...  | ....*...*..  |
|  ....**..... |  ...*****... | ....*****..  | ...*.......  |
|  ...**.***.. |  ...*....*.. | ...**.***..  | ...*....*..  |
|  ....*****.. |  ...*....... | ....**.....  | ...*****...  |
|  .....***... |  ....*...*.. | ...........  | ...........  |
|  ........... |  ......*.... | ...........  | ...........  |
|  ........... |  ........... | ...........  | ...........  |
|  ........... |  ........... | ...........  | ...........  |

The starting rows are valid 2c/4 GSE and they're nonzero, but they include a disconnect and I cannot think of any easy way to filter all such things. If that were solvable it seems maybe similar-ish to the odd-but-not-gutter case (could maybe closure c/2 center starts and start from first non-c/2 row after that).

The setup for unstaggered height window GSE start is a little weird to reason about. The intersection of the obvious constraint:

Code: Select all

|  ..WWWWWWWW... |  ..WWWWWWWW... | ...WWWWWWWW..  | ...WWWWWWWW..  |

...and its GS flip (which it must obey because we want the above constraint applied to the flipped copy of us above the axis):

Code: Select all

|  ...WWWWWWWW.. |  ...WWWWWWWW.. | ..WWWWWWWW...  | ..WWWWWWWW...  |

...is just the 2c/4 staggered height 7 constraint:

Code: Select all

|  ...WWWWWWW... |  ...WWWWWWW... | ...WWWWWWW...  | ...WWWWWWW...  |

Run in the obvious fashion this has 8 disconnected but non-zero center starts. I tried adding in 8 separate forbid_grid filters for them but it did not really work. They're (all? mostly? at least some) still findable in search state, I assume due to chimerism making each piece of each part of some other partial. Maybe a fancier filter that knew multiple grids and could filter state bits that are not part of some partial that mismatches all of them at once could do it?

It's also possible splitting input files one wildcard at a time and excluding the undesireable starts that way could do it, but it'd be a great deal of custom work and my money is probably on no ship existing anyway.

[amling]

c/6 height 7 1/3 filled memory and died.

I came back to this and gave it 1 TB but still no new results. It confirms (this was already known) no height 8, with longest partial:

Code: Select all

x = 91, y = 53, rule = LifeHistory
F.12B.F.12B.F.12B.F.12B.F.12B.F.12B.F$F.12B.F.12B.F.12B.F.12B.F.12B.F
.12B.F$F.12B.F.5BA6B.F.12B.F.5BA6B.F.12B.F.12B.F$F.4B3A5B.F.5BA6B.F.
4B3A5B.F.5BA6B.F.4B2A6B.F.4B2A6B.F$F.12B.F.5BA6B.F.12B.F.4BA7B.F.4BAB
A5B.F.3B2ABA5B.F$F.12B.F.12B.F.5B2A5B.F.5B2A5B.F.4BABA5B.F.3B2A7B.F$F
.4B2A6B.F.5B2A5B.F.5B2A5B.F.5B2A5B.F.4BA7B.F.4BABA5B.F$F.6B2A4B.F.5B
2A5B.F.12B.F.5BA6B.F.5B2A5B.F.5BA6B.F$F.12B.F.6B2A4B.F.5BABA4B.F.12B.
F.12B.F.7BA4B.F$F.7BA4B.F.7BA4B.F.8BA3B.F.6BABA3B.F.5B3A4B.F.5BABA4B.
F$F.6BABA3B.F.6BABA3B.F.6BABA3B.F.5B2A5B.F.5B3A4B.F.12B.F$F.6B3A3B.F.
6BABA3B.F.5B2A5B.F.12B.F.6BA5B.F.5B3A4B.F$F.12B.F.6BA5B.F.5B3A4B.F.7B
A4B.F.12B.F.6BA5B.F$F.6BA5B.F.5BA6B.F.4B2A6B.F.4B2A6B.F.4B3A5B.F.4BAB
A5B.F$F.4B2A6B.F.4B2ABA4B.F.12B.F.4B2A6B.F.4B2A6B.F.3BA8B.F$F.5BAB2A
3B.F.4B3A5B.F.4BA7B.F.12B.F.4BABA5B.F.4BABA5B.F$F.12B.F.6B2A4B.F.6B2A
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F.2B3A4BA2B.F.3BA2B2A4B.F.4BABAB2A2B.F14.F14.F14.F!

Height 8 1/6 hit 1 TB and died.