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A099733 a(n) is the number of active cells after a solid n X n square has reached a static state or constant population, closed and infinite loop in Conway's Game of Life. 2
0, 4, 12, 0, 24, 8, 12, 0, 52, 8, 12, 0, 4, 8, 0, 56, 72, 40, 60, 0, 52, 24, 92, 48, 28, 96, 312, 40 (list; graph; refs; listen; history; text; internal format)



Starting population for n is n^2.

a(n)=0 for n={1,4,8,12,15,20,..?..}, meaning that after a particular, finite number of generations, the grid is forever empty.

a(n) reaches a nonempty, single static state after a particular, finite number of generations for n={2,5,6,10,13,14,16,18,22,24,26,27,28,..?..}.

a(n) enters a constant population, infinite, two-state and closed loop after a particular, finite number of generations for n={3,7,9,11,17,19,21,23,25,..?..}.

For even generations > 153, a(29)=128. For odd generations > 153, a(29)=120. n=29 is the first value of a(n) for which the system enters a two-state loop with variable population after a particular, finite number of generations.


Table of n, a(n) for n=1..28.

Eric Weisstein's World of Mathematics, Game of Life


a(5)=24 because a 5 X 5 solid square placed on an otherwise empty grid at generation 0 in Conway's Game of Life will enter a static state at generation 11 with 24 cells forever alive/active/on.


Sequence in context: A255383 A218858 A014458 * A350259 A330989 A073902

Adjacent sequences:  A099730 A099731 A099732 * A099734 A099735 A099736




Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 08 2004



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Last modified January 23 03:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)