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A273910 Binary 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 614", based on the 5-celled von Neumann neighborhood.

%I A273910 #8 Feb 16 2025 08:33:36
%S A273910 1,11,101,1011,10001,110111,1000101,11011011,100000001,1100000111,
%T A273910 10100010101,101101101011,1000000010001,11000001110111,
%U A273910 101000101000101,1011011011011011,10000000000000001,110000000000000111,1010000000000010101,10110000000001101011
%N A273910 Binary 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 614", based on the 5-celled von Neumann neighborhood.
%C A273910 Initialized with a single black (ON) cell at stage zero.
%D A273910 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A273910 Robert Price, <a href="/A273910/b273910.txt">Table of n, a(n) for n = 0..126</a>
%H A273910 Robert Price, <a href="/A273910/a273910.tmp.txt">Diagrams of the first 20 stages</a>
%H A273910 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 A273910 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A273910 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A273910 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A273910 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A273910 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A273910 CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
%t A273910 code=614; stages=128;
%t A273910 rule=IntegerDigits[code,2,10];
%t A273910 g=2*stages+1; (* Maximum size of grid *)
%t A273910 a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *)
%t A273910 ca=a;
%t A273910 ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}];
%t A273910 PrependTo[ca,a];
%t A273910 (* Trim full grid to reflect growth by one cell at each stage *)
%t A273910 k=(Length[ca[[1]]]+1)/2;
%t A273910 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 A273910 Table[FromDigits[Part[ca[[i]][[i]],Range[i,2*i-1]],10], {i,1,stages-1}]
%K A273910 nonn,easy
%O A273910 0,2
%A A273910 _Robert Price_, Jun 03 2016