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%I A279999 #8 Dec 24 2016 10:54:50
%S A279999 1,0,7,2,25,20,3,214,141,152,1463,874,5825,3516,23387,13878,93549,
%T A279999 56024,374199,224106,1492673,912828,5921627,3618358,23752045,13949656,
%U A279999 95008183,55796586,380032705,223194556,1520114523,892794422,6080507245,3571030744
%N A279999 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 233", based on the 5-celled von Neumann neighborhood.
%C A279999 Initialized with a single black (ON) cell at stage zero.
%D A279999 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A279999 Robert Price, <a href="/A279999/b279999.txt">Table of n, a(n) for n = 0..126</a>
%H A279999 Robert Price, <a href="/A279999/a279999.tmp.txt">Diagrams of first 20 stages</a>
%H A279999 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 A279999 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A279999 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A279999 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A279999 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A279999 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A279999 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A279999 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A279999 code = 233; stages = 128;
%t A279999 rule = IntegerDigits[code, 2, 10];
%t A279999 g = 2 * stages + 1; (* Maximum size of grid *)
%t A279999 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A279999 ca = a;
%t A279999 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A279999 PrependTo[ca, a];
%t A279999 (* Trim full grid to reflect growth by one cell at each stage *)
%t A279999 k = (Length[ca[[1]]] + 1)/2;
%t A279999 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 A279999 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 2], {i ,1, stages - 1}]
%Y A279999 Cf. A279996, A279997, A279998.
%K A279999 nonn,easy
%O A279999 0,3
%A A279999 _Robert Price_, Dec 24 2016

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