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A289767 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 598", based on the 5-celled von Neumann neighborhood.

%I A289767 #8 Feb 16 2025 08:33:49
%S A289767 1,10,110,1100,10100,101000,1011000,10110000,100010000,1000100000,
%T A289767 11011100000,110111000000,1000101000000,10001010000000,
%U A289767 110110110000000,1101101100000000,10000000100000000,100000001000000000,1100000111000000000,11000001110000000000
%N A289767 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 598", based on the 5-celled von Neumann neighborhood.
%C A289767 Initialized with a single black (ON) cell at stage zero.
%D A289767 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A289767 Robert Price, <a href="/A289767/b289767.txt">Table of n, a(n) for n = 0..126</a>
%H A289767 Robert Price, <a href="/A289767/a289767.tmp.txt">Diagrams of first 20 stages</a>
%H A289767 N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015
%H A289767 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A289767 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A289767 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A289767 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A289767 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A289767 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A289767 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A289767 code = 598; stages = 128;
%t A289767 rule = IntegerDigits[code, 2, 10];
%t A289767 g = 2 * stages + 1; (* Maximum size of grid *)
%t A289767 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A289767 ca = a;
%t A289767 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A289767 PrependTo[ca, a];
%t A289767 (* Trim full grid to reflect growth by one cell at each stage *)
%t A289767 k = (Length[ca[[1]]] + 1)/2;
%t A289767 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 A289767 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}]
%Y A289767 Cf. A289766, A289768, A289769.
%K A289767 nonn,easy
%O A289767 0,2
%A A289767 _Robert Price_, Jul 12 2017