Density

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.

References

• http://www.argentum.freeserve.co.uk/dense.htm
• http://www.ai.sri.com/~nysmith/life/