# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a280146 Showing 1-1 of 1 %I A280146 #8 Dec 27 2016 23:17:33 %S A280146 1,10,101,1010,10101,101010,1010101,10101010,101010101,1010101010, %T A280146 10101010101,101010101010,1010101010101,10101110101010, %U A280146 101010101010101,1011111110101010,10100000101010101,101011101110101010,1010000010101010101,10111111111110101010 %N A280146 Binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 243", based on the 5-celled von Neumann neighborhood. %C A280146 Initialized with a single black (ON) cell at stage zero. %D A280146 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. %H A280146 Robert Price, Table of n, a(n) for n = 0..126 %H A280146 Robert Price, Diagrams of first 20 stages %H A280146 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 %H A280146 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton %H A280146 S. Wolfram, A New Kind of Science %H A280146 Wolfram Research, Wolfram Atlas of Simple Programs %H A280146 Index entries for sequences related to cellular automata %H A280146 Index to 2D 5-Neighbor Cellular Automata %H A280146 Index to Elementary Cellular Automata %t A280146 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}]; %t A280146 code = 243; stages = 128; %t A280146 rule = IntegerDigits[code, 2, 10]; %t A280146 g = 2 * stages + 1; (* Maximum size of grid *) %t A280146 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *) %t A280146 ca = a; %t A280146 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}]; %t A280146 PrependTo[ca, a]; %t A280146 (* Trim full grid to reflect growth by one cell at each stage *) %t A280146 k = (Length[ca[[1]]] + 1)/2; %t A280146 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 A280146 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}] %Y A280146 Cf. A280145, A280147, A280148. %K A280146 nonn,easy %O A280146 0,2 %A A280146 _Robert Price_, Dec 26 2016 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE