# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a289969 Showing 1-1 of 1 %I A289969 #8 Jul 17 2017 08:26:28 %S A289969 1,2,6,15,31,60,124,255,511,1022,2046,4095,8191,16358,32742,65535, %T A289969 131071,262015,524159,1048455,2097031,4194168,8388472,16777095, %U A289969 33554311,67107704,134216568,268435335,536870791,1073741816,2147483640,4294967239,8589934535 %N A289969 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 629", based on the 5-celled von Neumann neighborhood. %C A289969 Initialized with a single black (ON) cell at stage zero. %D A289969 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. %H A289969 Robert Price, Table of n, a(n) for n = 0..126 %H A289969 Robert Price, Diagrams of first 20 stages %H A289969 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 %H A289969 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton %H A289969 S. Wolfram, A New Kind of Science %H A289969 Wolfram Research, Wolfram Atlas of Simple Programs %H A289969 Index entries for sequences related to cellular automata %H A289969 Index to 2D 5-Neighbor Cellular Automata %H A289969 Index to Elementary Cellular Automata %t A289969 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}]; %t A289969 code = 629; stages = 128; %t A289969 rule = IntegerDigits[code, 2, 10]; %t A289969 g = 2 * stages + 1; (* Maximum size of grid *) %t A289969 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *) %t A289969 ca = a; %t A289969 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}]; %t A289969 PrependTo[ca, a]; %t A289969 (* Trim full grid to reflect growth by one cell at each stage *) %t A289969 k = (Length[ca[[1]]] + 1)/2; %t A289969 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 A289969 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}] %Y A289969 Cf. A289967, A289968, A289970. %K A289969 nonn,easy %O A289969 0,2 %A A289969 _Robert Price_, Jul 16 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE