

A205599


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


0



1, 2, 2, 2, 1, 2, 14, 4, 22, 2, 121, 5, 143, 14, 55, 26, 17, 22, 171, 180, 189, 198, 207
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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. 255260, p. 281285


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: A205013 A138258 A308367 * A327891 A265671 A214707
Adjacent sequences: A205596 A205597 A205598 * A205600 A205601 A205602


KEYWORD

nonn,hard


AUTHOR

Ben Branman, Jan 29 2012


STATUS

approved



