# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a286699 Showing 1-1 of 1 %I A286699 #7 May 12 2017 23:15:16 %S A286699 1,1,100,111,10000,1111,1100000,111111,110000000,111111,11110000000, %T A286699 11111111,1111000000000,1111111111,111100000000000,111111111111, %U A286699 11110000000000000,1111111111,1111111100000000000,111111111111,111111110000000000000,11111111111111 %N A286699 Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 209", based on the 5-celled von Neumann neighborhood. %C A286699 Initialized with a single black (ON) cell at stage zero. %D A286699 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. %H A286699 Robert Price, Table of n, a(n) for n = 0..126 %H A286699 Robert Price, Diagrams of first 20 stages %H A286699 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 %H A286699 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton %H A286699 S. Wolfram, A New Kind of Science %H A286699 Wolfram Research, Wolfram Atlas of Simple Programs %H A286699 Index entries for sequences related to cellular automata %H A286699 Index to 2D 5-Neighbor Cellular Automata %H A286699 Index to Elementary Cellular Automata %t A286699 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}]; %t A286699 code = 209; stages = 128; %t A286699 rule = IntegerDigits[code, 2, 10]; %t A286699 g = 2 * stages + 1; (* Maximum size of grid *) %t A286699 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *) %t A286699 ca = a; %t A286699 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}]; %t A286699 PrependTo[ca, a]; %t A286699 (* Trim full grid to reflect growth by one cell at each stage *) %t A286699 k = (Length[ca[[1]]] + 1)/2; %t A286699 ca = Table[Table[Part[ca[[n]] [[j]],Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}]; %t A286699 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}] %Y A286699 Cf. A286698, A286700, A286701. %K A286699 nonn,easy %O A286699 0,3 %A A286699 _Robert Price_, May 12 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE