A205599 - OEIS

%I #8 Mar 30 2012 19:00:48

%S 1,2,2,2,1,2,14,4,22,2,121,5,143,14,55,26,17,22,171,180,189,198,207

%N Maximum period of the totalistic 2-color radius 2 cellular automaton in a cyclic universe of width n.

%C A cell's neighborhood consists of itself, the two cells to its left, and the two cells to its right.  A cell becomes live if it had either two or four live neighbors (including itself) in the previous generation.

%D Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, 2002, p. 255-260, p. 281-285

%e For n=7, the initial state 0, 0, 1, 1, 0, 1, 0 has evolution:

%e 0011010

%e 1110010

%e 1000110

%e 1011100

%e 1010001

%e 0010111

%e 0110100

%e 1100101

%e 0001101

%e 0111001

%e 0100011

%e 0101110

%e 1101000

%e 1001011

%e 0011010

%e Which has period 14, the highest possible.  Thus a(7)=14.

%t f[list_] := -Subtract @@ Flatten[Map[Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[{20, {2, 1}, 2}], list, Unequal, All], {0}]]; a[n_] := Max[Table[f[IntegerDigits[i, 2, n]], {i, 0, 2^n - 1}]]; Table[a[n], {n, 1, 12}]

%Y Cf. A204371, A204714.

%K nonn,hard

%O 1,2

%A _Ben Branman_, Jan 29 2012