1,1

New state of cell is 1 in every case except when the previous states of the cell and its two neighbors were all the same, or when the left neighbor was 1 and the cell and its right neighbor were both 0.

A cellular automaton using Rule 110 with arbitrary inputs is a universal Turing machine.

Row n has length n.

Comment from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 27 2007 (Start): An alternative method of producing this sequence. Let a(n,m)=A047999(n,m), b(n,m)=Gray_code[n,m], c(n,m)=By_terms[a(n,m)*b(n,m)].

In Mathematica language: Clear[a] n0 = 10 a = Table[Table[Mod[Binomial[n, m], 2], {m, 0, n0 + 1}], {n, 0, n0 + 1}]

(* Gray Code*) b = Table[Table[If[m <= n && m > 1, Mod[a[[n, m]] + a[[n, m + 1]], 2], If[n == m, 1, 1]], {m, 1, n0 + 1}], {n, 1, n0 + 1}]

(*A047999 Pascal's triangle modulo two*) c = Table[Table[Mod[Binomial[n, m], 2], {m, 0, n0}], {n, 0, n0}] d = Table[Table[If[m > 1, c[[n, m]]*b[[n, m]], 1], {m, 1, n}], {n, 1, n0 + 1}] Flatten[d] (End)

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 31ff..

Index entries for sequences related to cellular automata

Eric Weisstein's World of Mathematics, Rule 110

1; 1,1; 1,1,1; 1,1,0,1; 1,1,1,1,1; ...

Cf. A070950, A070886.

Cf. A047999.

Sequence in context: A071374 A077010 A166280 this_sequence A110242 A131364 A054527

Adjacent sequences: A070884 A070885 A070886 this_sequence A070888 A070889 A070890

nonn,tabf,nice,easy

N. J. A. Sloane (njas(AT)research.att.com), May 19 2002

More terms from Hans Havermann (pxp(AT)rogers.com), May 26 2002