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A279723 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 193", based on the 5-celled von Neumann neighborhood.

%I A279723 #8 Feb 16 2025 08:33:38
%S A279723 1,0,7,0,31,0,127,0,511,0,2047,0,8191,0,31999,0,114943,15360,445695,
%T A279723 61440,1573119,523264,7868415,1044480,29364223,8187904,117444607,
%U A279723 32763904,402657279,350220288,3327,3684691968,12543,14700973056,50593023,59054751744,1044735
%N A279723 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 193", based on the 5-celled von Neumann neighborhood.
%C A279723 Initialized with a single black (ON) cell at stage zero.
%D A279723 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A279723 Robert Price, <a href="/A279723/b279723.txt">Table of n, a(n) for n = 0..126</a>
%H A279723 Robert Price, <a href="/A279723/a279723.tmp.txt">Diagrams of first 20 stages</a>
%H A279723 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 A279723 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A279723 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A279723 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A279723 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A279723 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A279723 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A279723 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A279723 code = 193; stages = 128;
%t A279723 rule = IntegerDigits[code, 2, 10];
%t A279723 g = 2 * stages + 1; (* Maximum size of grid *)
%t A279723 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A279723 ca = a;
%t A279723 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A279723 PrependTo[ca, a];
%t A279723 (* Trim full grid to reflect growth by one cell at each stage *)
%t A279723 k = (Length[ca[[1]]] + 1)/2;
%t A279723 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 A279723 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 2], {i ,1, stages - 1}]
%Y A279723 Cf. A279720, A279721, A279722.
%K A279723 nonn,easy
%O A279723 0,3
%A A279723 _Robert Price_, Dec 17 2016