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%I A279998 #8 Dec 24 2016 10:54:43
%S A279998 1,0,7,4,19,10,96,107,354,100,1901,1388,4205,3948,28013,27756,93549,
%T A279998 28012,486765,355692,1076333,1011180,7171373,7105772,23948461,7171244,
%U A279998 124611757,90991788,275606701,258829484,1835822253,1819241644,6130592941,1835429036
%N A279998 Decimal 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 233", based on the 5-celled von Neumann neighborhood.
%C A279998 Initialized with a single black (ON) cell at stage zero.
%D A279998 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A279998 Robert Price, <a href="/A279998/b279998.txt">Table of n, a(n) for n = 0..126</a>
%H A279998 Robert Price, <a href="/A279998/a279998.tmp.txt">Diagrams of first 20 stages</a>
%H A279998 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 A279998 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A279998 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A279998 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A279998 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A279998 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A279998 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A279998 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A279998 code = 233; stages = 128;
%t A279998 rule = IntegerDigits[code, 2, 10];
%t A279998 g = 2 * stages + 1; (* Maximum size of grid *)
%t A279998 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A279998 ca = a;
%t A279998 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A279998 PrependTo[ca, a];
%t A279998 (* Trim full grid to reflect growth by one cell at each stage *)
%t A279998 k = (Length[ca[[1]]] + 1)/2;
%t A279998 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 A279998 Table[FromDigits[Part[ca[[i]] [[i]], Range[1, i]], 2], {i, 1, stages - 1}]
%Y A279998 Cf. A279996, A279997, A279999.
%K A279998 nonn,easy
%O A279998 0,3
%A A279998 _Robert Price_, Dec 24 2016

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