Density: Difference between revisions
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let's append patterns |
Come on, complete the demonstrations (JLS searching black-white reversal with population constraint works) |
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| 6 || 0.5 || 18 (eg. two [[long shillelagh]]s) || {{EmbedViewer|pname=twolongshillelaghs}}<br>{{EmbedViewer|rle=2o2b2o$o2bobo$bob2o$2o$2b2obo$2bob2o!}} | | 6 || 0.5 || 18 (eg. two [[long shillelagh]]s) || {{EmbedViewer|pname=twolongshillelaghs}}<br>{{EmbedViewer|rle=2o2b2o$o2bobo$bob2o$2o$2b2obo$2bob2o!}} | ||
|- | |- | ||
| 7 || 0.5714 || 28 | | 7 || 0.5714 || 28 || {{EmbedViewer|rle=ob2ob2o$2obobo$3bo2bo$3ob3o$o2bo$bobob2o$2ob2obo!}} | ||
|- | |- | ||
| 8 || 0.5625 || 36 (eg. nine blocks) || {{EmbedViewer|rle=2ob2ob2o$2ob2ob2o2$2ob2ob2o$2ob2ob2o2$2ob2ob2o$2ob2ob2o!}} | | 8 || 0.5625 || 36 (eg. nine blocks) || {{EmbedViewer|rle=2ob2ob2o$2ob2ob2o2$2ob2ob2o$2ob2ob2o2$2ob2ob2o$2ob2ob2o!}} | ||
|- | |- | ||
| 9 || 0.5309 || 43 | | 9 || 0.5309 || 43 || {{EmbedViewer|rle=2o2b2ob2o11b2o2b2ob2o11bob2ob2obo11bob2ob2obo11bob2obob2o$o2bobob2o11b | ||
o2bobob2o11b2obobob2o11b2obobob2o11b2obob2obo$bobobo15bobobo17bobo17bo | |||
bo17bo$2obob4o11b2obob4o11b2obob4o11b2obob4o11b3ob4o$o2bo4bo12bobo4bo | |||
12bobo4bo11bo2bo4bo11bo2bo4bo$bob4o14bob4o14bob4o14bob4o14bobob4o$2o4b | |||
2o12b2o4b2o12b2o4b2o12b2o4b2o12b2obobo$o2b2o3bo11bo2b2o3bo11bo2b2o3bo | |||
11bo2b2o3bo11bo2bobob2o$b2ob2ob2o12b2ob2ob2o12b2ob2ob2o12b2ob2ob2o13b | |||
2ob2obo12$ob2ob2obo11bob2ob2obo11bob2ob2obo11bob2ob2obo11bob2ob2obo$2o | |||
bobob2o11b2obobob2o11b2obobob2o11b2obobob2o11b2obobob2o$3bobo17bobo17b | |||
obo17bobo17bobo$2obob4o11b4ob4o11b2obob4o11b4o2b3o11b4ob4o$2obo4bo11bo | |||
7bo11bob2o4bo11bo3b2o2bo11bo7bo$3b5o13bob5o16b4o13b3o2b2o13b7o$3o17b2o | |||
bo17b3o20bo$o2bob2obo11bo2bob2obo11bo2bob2obo11bob2ob2obo11bob2ob2obo$ | |||
2b2obob2o13b2obob2o11b2o2b2ob2o11b2obobob2o11b2obobob2o!}} | |||
|- | |- | ||
| 10 || 0.5400 || 54 | | 10 || 0.5400 || 54 | ||
Revision as of 06:10, 17 January 2021
The density of a pattern is the proportion of live cells within its bounding box.
The maximal densities of square (pseudo) still lifes up to 20×20 are:
| Side length | Max. density | Max. population | Pattern |
|---|---|---|---|
| 1 | 0 | 0 | |
| 2 | 1 | 4 (block) | |
| 3 | 0.6̄ | 6 (ship) | |
| 4 | 0.5 | 8 (pond, long ship) | |
| 5 | 0.64 | 16 (four blocks) | (click above to open LifeViewer) |
| 6 | 0.5 | 18 (eg. two long shillelaghs) | (click above to open LifeViewer) |
| 7 | 0.5714 | 28 | (click above to open LifeViewer) |
| 8 | 0.5625 | 36 (eg. nine blocks) | (click above to open LifeViewer) |
| 9 | 0.5309 | 43 | (click above to open LifeViewer) |
| 10 | 0.5400 | 54 | |
| 11 | 0.5289 | 64 | |
| 12 | 0.5278 | 76 | |
| 13 | 0.5325 | 90 | |
| 14 | 0.5306 | 104 | |
| 15 | 0.5289 | 119 | |
| 16 | 0.531 | 136 | |
| 17 | 0.526 | 152 | |
| 18 | 0.528 | 171 | |
| 19 | 0.526 | 190 | |
| 20 | 0.525 | 210 |
For any side length of the form 3n-1, a segment of block agar can be used to reach a population of 4n². Up to n = 4 this is the optimal solution.