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A279722 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 193", based on the 5-celled von Neumann neighborhood.

%I A279722 #8 Feb 16 2025 08:33:38
%S A279722 1,0,7,0,31,0,127,0,511,0,2047,0,8191,0,32671,0,130567,240,522651,240,
%T A279722 2088963,4088,8386575,4080,33546247,15608,134184967,64760,536739843,
%U A279722 261834,2140667904,1047003,8557953024,12841179,34258945536,65499,136935505920
%N A279722 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 193", based on the 5-celled von Neumann neighborhood.
%C A279722 Initialized with a single black (ON) cell at stage zero.
%D A279722 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A279722 Robert Price, <a href="/A279722/b279722.txt">Table of n, a(n) for n = 0..126</a>
%H A279722 Robert Price, <a href="/A279722/a279722.tmp.txt">Diagrams of first 20 stages</a>
%H A279722 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 A279722 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A279722 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A279722 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A279722 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A279722 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A279722 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A279722 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A279722 code = 193; stages = 128;
%t A279722 rule = IntegerDigits[code, 2, 10];
%t A279722 g = 2 * stages + 1; (* Maximum size of grid *)
%t A279722 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A279722 ca = a;
%t A279722 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A279722 PrependTo[ca, a];
%t A279722 (* Trim full grid to reflect growth by one cell at each stage *)
%t A279722 k = (Length[ca[[1]]] + 1)/2;
%t A279722 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 A279722 Table[FromDigits[Part[ca[[i]] [[i]], Range[1, i]], 2], {i, 1, stages - 1}]
%Y A279722 Cf. A279720, A279721, A279723.
%K A279722 nonn,easy
%O A279722 0,3
%A A279722 _Robert Price_, Dec 17 2016