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A279716 Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 189", based on the 5-celled von Neumann neighborhood.

%I A279716 #8 Feb 16 2025 08:33:38
%S A279716 1,10,10,1100,101,111000,1011,11110010,10000,1111100111,100100,
%T A279716 111111000011,1011010,11111110011000,10011011,1111111100011010,
%U A279716 101011000,111111111001011011,1001011110,11111111110000010110,10111100110,1111111111100100110110,100101110110
%N A279716 Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 189", based on the 5-celled von Neumann neighborhood.
%C A279716 Initialized with a single black (ON) cell at stage zero.
%D A279716 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A279716 Robert Price, <a href="/A279716/b279716.txt">Table of n, a(n) for n = 0..126</a>
%H A279716 Robert Price, <a href="/A279716/a279716.tmp.txt">Diagrams of first 20 stages</a>
%H A279716 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 A279716 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A279716 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A279716 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A279716 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A279716 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A279716 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A279716 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A279716 code = 189; stages = 128;
%t A279716 rule = IntegerDigits[code, 2, 10];
%t A279716 g = 2 * stages + 1; (* Maximum size of grid *)
%t A279716 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A279716 ca = a;
%t A279716 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A279716 PrependTo[ca, a];
%t A279716 (* Trim full grid to reflect growth by one cell at each stage *)
%t A279716 k = (Length[ca[[1]]] + 1)/2;
%t A279716 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 A279716 Table[FromDigits[Part[ca[[i]] [[i]], Range[1, i]], 10], {i, 1, stages - 1}]
%Y A279716 Cf. A279717, A279718, A279719.
%K A279716 nonn,easy
%O A279716 0,2
%A A279716 _Robert Price_, Dec 17 2016