cp's OEIS Frontend

A287197 Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 259", based on the 5-celled von Neumann neighborhood.

%I A287197 #12 Feb 16 2025 08:33:46
%S A287197 1,3,1,12,1,60,1,252,1,1020,1,4092,1,16380,1,65532,1,262140,1,1048572,
%T A287197 1,4194300,1,16777212,1,67108860,1,268435452,1,1073741820,1,
%U A287197 4294967292,1,17179869180,1,68719476732,1,274877906940,1,1099511627772,1,4398046511100,1
%N A287197 Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 259", based on the 5-celled von Neumann neighborhood.
%C A287197 Initialized with a single black (ON) cell at stage zero.
%C A287197 Appears to differ from A277799 only at a(1). - _R. J. Mathar_, May 25 2017
%D A287197 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A287197 Robert Price, <a href="/A287197/b287197.txt">Table of n, a(n) for n = 0..126</a>
%H A287197 Robert Price, <a href="/A287197/a287197.tmp.txt">Diagrams of first 20 stages</a>
%H A287197 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 A287197 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A287197 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A287197 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A287197 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A287197 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A287197 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A287197 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A287197 code = 259; stages = 128;
%t A287197 rule = IntegerDigits[code, 2, 10];
%t A287197 g = 2 * stages + 1; (* Maximum size of grid *)
%t A287197 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A287197 ca = a;
%t A287197 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A287197 PrependTo[ca, a];
%t A287197 (* Trim full grid to reflect growth by one cell at each stage *)
%t A287197 k = (Length[ca[[1]]] + 1)/2;
%t A287197 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 A287197 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}]
%Y A287197 Cf. A287194, A287196, A287199.
%K A287197 nonn,easy
%O A287197 0,2
%A A287197 _Robert Price_, May 21 2017