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%I A281105 #7 Jan 15 2017 11:50:29
%S A281105 1,1,5,1,5,17,85,65,325,81,277,1345,5445,5201,21781,21825,86085,86353,
%T A281105 332821,349249,1377605,1381457,5588245,5592385,22368325,22368593,
%U A281105 89461781,89478209,357844293,357913681,1431307541,1431311681,5726294085,5726359889
%N A281105 Decimal 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 324", based on the 5-celled von Neumann neighborhood.
%C A281105 Initialized with a single black (ON) cell at stage zero.
%D A281105 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A281105 Robert Price, <a href="/A281105/b281105.txt">Table of n, a(n) for n = 0..126</a>
%H A281105 Robert Price, <a href="/A281105/a281105.tmp.txt">Diagrams of first 20 stages</a>
%H A281105 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 A281105 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A281105 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A281105 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A281105 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A281105 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A281105 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A281105 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A281105 code = 324; stages = 128;
%t A281105 rule = IntegerDigits[code, 2, 10];
%t A281105 g = 2 * stages + 1; (* Maximum size of grid *)
%t A281105 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A281105 ca = a;
%t A281105 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A281105 PrependTo[ca, a];
%t A281105 (* Trim full grid to reflect growth by one cell at each stage *)
%t A281105 k = (Length[ca[[1]]] + 1)/2;
%t A281105 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 A281105 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 2], {i ,1, stages - 1}]
%Y A281105 Cf. A281102, A281103, A281104.
%K A281105 nonn,easy
%O A281105 0,3
%A A281105 _Robert Price_, Jan 14 2017

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