Difference between revisions of "Density"
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{{Glossary}} | |||
The '''density''' of a pattern is the proportion of live cells within its [[bounding box]]. | The '''density''' of a pattern is the proportion of live cells within its [[bounding box]]. | ||
Revision as of 20:18, 13 March 2014
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 |
---|---|---|
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) |
6 | 0.5 | 18 (eg. two long shillelaghs) |
7 | 0.5714 | 28 |
8 | 0.5625 | 36 (eg. nine blocks) |
9 | 0.5309 | 43 |
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.