A205599 Maximum period of the totalistic 2-color radius 2 cellular automaton in a cyclic universe of width n.

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

Offset

1,2

Comments

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.

References

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

Links

Table of n, a(n) for n=1..23.

Example

For n=7, the initial state 0, 0, 1, 1, 0, 1, 0 has evolution:
0011010
1110010
1000110
1011100
1010001
0010111
0110100
1100101
0001101
0111001
0100011
0101110
1101000
1001011
0011010
Which has period 14, the highest possible.  Thus a(7)=14.

Mathematica

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}]

Crossrefs

Cf. A204371, A204714.

Sequence in context: A138258 A359812 A308367 * A327891 A265671 A214707

Adjacent sequences: A205596 A205597 A205598 * A205600 A205601 A205602

Keyword

nonn,hard

Author

Ben Branman, Jan 29 2012

Status

approved