# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a290678 Showing 1-1 of 1 %I A290678 #7 Aug 09 2017 07:47:01 %S A290678 1,1,3,1,7,1,15,5,31,5,63,21,127,29,255,73,511,73,1023,329,2047,457, %T A290678 4095,1161,8191,1193,16383,5369,32767,7281,65535,18725,131071,18725, %U A290678 262143,84261,524287,117029,1048575,297253,2097151,305445,4194303,1374501,8388607 %N A290678 Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 926", based on the 5-celled von Neumann neighborhood. %C A290678 Initialized with a single black (ON) cell at stage zero. %D A290678 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. %H A290678 Robert Price, Table of n, a(n) for n = 0..126 %H A290678 Robert Price, Diagrams of first 20 stages %H A290678 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 %H A290678 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton %H A290678 S. Wolfram, A New Kind of Science %H A290678 Wolfram Research, Wolfram Atlas of Simple Programs %H A290678 Index entries for sequences related to cellular automata %H A290678 Index to 2D 5-Neighbor Cellular Automata %H A290678 Index to Elementary Cellular Automata %t A290678 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}]; %t A290678 code = 926; stages = 128; %t A290678 rule = IntegerDigits[code, 2, 10]; %t A290678 g = 2 * stages + 1; (* Maximum size of grid *) %t A290678 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *) %t A290678 ca = a; %t A290678 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}]; %t A290678 PrependTo[ca, a]; %t A290678 (* Trim full grid to reflect growth by one cell at each stage *) %t A290678 k = (Length[ca[[1]]] + 1)/2; %t A290678 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 A290678 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}] %Y A290678 Cf. A290676, A290677, A290679. %K A290678 nonn,easy %O A290678 0,3 %A A290678 _Robert Price_, Aug 09 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE