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A205599 Maximum period of the totalistic 2-color 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 (list; graph; refs; listen; history; text; internal format)
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: A124369 A205013 A138258 * A265671 A214707 A083039

Adjacent sequences:  A205596 A205597 A205598 * A205600 A205601 A205602

KEYWORD

nonn,hard

AUTHOR

Ben Branman, Jan 29 2012

STATUS

approved

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Last modified February 24 07:50 EST 2018. Contains 299599 sequences. (Running on oeis4.)