Search: id:A070887
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%I A070887
%S A070887 1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,1,1,1,1,0,1,0,
%T A070887 1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,1,1,0,1,
%U A070887 1,1,0,1,0,0,0,1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0,1,0,1
%N A070887 Triangle read by rows giving successive states of cellular automaton 
               generated by "Rule 110".
%C A070887 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.
%C A070887 A cellular automaton using Rule 110 with arbitrary inputs is a universal 
               Turing machine.
%C A070887 Row n has length n.
%C A070887 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)].
%C A070887 In Mathematica language: Clear[a] n0 = 10 a = Table[Table[Mod[Binomial[n, 
               m], 2], {m, 0, n0 + 1}], {n, 0, n0 + 1}]
%C A070887 (* 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}]
%C A070887 (*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)
%D A070887 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 31ff..
%H A070887 <a href="Sindx_Ce.html#cell">Index entries for sequences related to cellular 
               automata</a>
%H A070887 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Rule110.html">Rule 110</a>
%e A070887 1; 1,1; 1,1,1; 1,1,0,1; 1,1,1,1,1; ...
%Y A070887 Cf. A070950, A070886.
%Y A070887 Cf. A047999.
%Y A070887 Sequence in context: A071374 A077010 A166280 this_sequence A110242 A131364 
               A054527
%Y A070887 Adjacent sequences: A070884 A070885 A070886 this_sequence A070888 A070889 
               A070890
%K A070887 nonn,tabf,nice,easy
%O A070887 1,1
%A A070887 N. J. A. Sloane (njas(AT)research.att.com), May 19 2002
%E A070887 More terms from Hans Havermann (pxp(AT)rogers.com), May 26 2002

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