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 lengthMax. densityMax. population
100
214 (block)
30.6̄6 (ship)
40.58 (pond, long ship)
50.6416 (four blocks)
60.518 (eg. two long shillelaghs)
70.571428
80.562536 (eg. nine blocks)
90.530943
100.540054
110.528964
120.527876
130.532590
140.5306104
150.5289119
160.531136
170.526152
180.528171
190.526190
200.525210

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

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