A204714 Maximum period of cellular automaton rule 54 in a cyclic universe of width n.
1, 1, 1, 4, 1, 4, 4, 8, 27, 30, 99, 12, 169, 112, 330, 40, 289, 306, 494, 86, 399, 484, 690, 312, 1800, 624, 918, 224, 783, 780, 1240, 608, 1056, 952, 1540, 684
Offset: 1
Keywords
Examples
For n=8, the initial condition 00011101 yields the evolution 00011101 10100011 01110100 10001110 11010001 00111010 01000111 11101000 00011101 Which is period 8, the maximum possible, so a(8)=8.
Links
- Index entries for sequences related to cellular automata
- Eric Weisstein's World of Mathematics, Rule 54
Programs
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Mathematica
f[list_] := -Subtract @@ Flatten[Map[Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[54], list, Unequal, All], {0}]]; a[n_] := Max[Table[f[IntegerDigits[i, 2, n]], {i, 0, 2^n - 1}]]; Table[a[n], {n, 1, 10}]
Extensions
a(15)-a(36) from Lars Blomberg, Dec 24 2015