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A273912 Binary 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 614", based on the 5-celled von Neumann neighborhood.

%I A273912 #7 Feb 16 2025 08:33:36
%S A273912 1,11,101,1101,10001,111011,1010001,11011011,100000001,1110000011,
%T A273912 10101000101,110101101101,1000100000001,11101110000011,
%U A273912 101000101000101,1101101101101101,10000000000000001,111000000000000011,1010100000000000101,11010110000000001101
%N A273912 Binary 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 614", based on the 5-celled von Neumann neighborhood.
%C A273912 Initialized with a single black (ON) cell at stage zero.
%D A273912 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A273912 Robert Price, <a href="/A273912/b273912.txt">Table of n, a(n) for n = 0..126</a>
%H A273912 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 A273912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A273912 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A273912 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A273912 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A273912 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A273912 CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
%t A273912 code=614; stages=128;
%t A273912 rule=IntegerDigits[code,2,10];
%t A273912 g=2*stages+1; (* Maximum size of grid *)
%t A273912 a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *)
%t A273912 ca=a;
%t A273912 ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}];
%t A273912 PrependTo[ca,a];
%t A273912 (* Trim full grid to reflect growth by one cell at each stage *)
%t A273912 k=(Length[ca[[1]]]+1)/2;
%t A273912 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 A273912 Table[FromDigits[Part[ca[[i]][[i]],Range[1,i]],10], {i,1,stages-1}]
%Y A273912 Cf. A273910.
%K A273912 nonn,easy
%O A273912 0,2
%A A273912 _Robert Price_, Jun 03 2016