A180001 Eventual period of a single cell in rule 110 cellular automaton in a cyclic universe of width n.
1, 1, 1, 2, 1, 9, 14, 16, 7, 25, 110, 9, 351, 91, 295, 32, 7, 27, 285, 30, 630, 44, 1058, 36, 250, 7, 405, 1652, 1044, 60, 7, 64, 495, 51, 1050, 72, 4403, 76, 390, 60, 7, 630, 1548, 88, 7, 7, 705, 96, 1470, 100, 765, 195, 8109, 7, 825, 7, 2052, 116, 7, 19560, 915
Offset: 1
Keywords
Examples
For n=4, the evolution of a single cell is: 0001 0011 0111 <--= period starts 1101 0111 <--= again start of period etc, so a(4)=2.
Links
- Pontus von Brömssen, Table of n, a(n) for n = 1..1000
- Eric Weisstein's World of Mathematics, Rule 110
- Index entries for sequences related to cellular automata
Programs
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Mathematica
a[n_] := -Subtract @@ Flatten[Map[Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[110], Prepend[Table[0, {n - 1}], 1], Unequal, All], {0}]] -
Sage
def A180001(n): def bit(x,i): return (x >> i) & 1 rulemap = dict((tuple(bit(i,k) for k in reversed(range(3))), bit(110,i)) for i in range(8)) def neighbours(d, i): return tuple(d[k % n] for k in [i-1..i+1]) v = [0]*n; v[-1] = 1; history = [v] while True: v2 = [rulemap[neighbours(history[-1], i)] for i in range(n)] if v2 in history: return len(history)-history.index(v2) history.append(v2) # D. S. McNeil, Jan 15 2011
Extensions
More terms from Alois P. Heinz, Jan 14 2011
Comments