A334497 Maximum value of eventual period for any starting configuration for a rule 30 cellular automaton in a cyclic universe of width n.

1, 1, 1, 8, 5, 1, 63, 40, 171, 15, 154, 102, 832, 1428, 1455, 6016, 10846, 2844, 3705, 6150, 2793, 3553, 38249, 185040, 588425, 312156, 240300, 249165, 1466066, 374265, 2841150, 2002272, 2038476, 5656002, 18480630, 2237472

Offset: 1

Author

N. J. A. Sloane, May 05 2020

Keywords

• nonn
• more

Comments

Bradley Klee computed a(1)-a(7).

References

• Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020.

Links

• Dustin Gage, Elizabeth Laub and Briana McGarry, Cellular Automata: Is Rule 30 Random?, 2005.

Crossrefs

Cf. A180001, A334496, A334499-A334515, A357950.

Programs

Mathematica

a[rule_, init_] := -Subtract @@ Flatten[Map[
     Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[rule],
      init, Unequal, All], {0}]]
tri[n_] := a[30, #] & /@ Tuples[{0, 1}, n];
tri /@ Range[7]
Max /@ %
(* Bradley Klee, Apr 26 2020 *)

Formula

a(n) <= A357950(n). Equality holds for n = 4, 8, 16. - Pontus von Brömssen, Oct 22 2022

Extensions

a(8)-a(12) from Jinyuan Wang, May 14 2020

a(13)-a(22) from Pontus von Brömssen, Oct 22 2022

a(23)-a(36) from Paolo Xausa, Jun 29 2023, using data from Gage, Laub and McGarry (2005), p. 7, Table 2.