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A277918 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 4", based on the 5-celled von Neumann neighborhood.

%I A277918 #7 Feb 16 2025 08:33:37
%S A277918 1,2,4,10,16,40,68,170,256,640,1088,2720,4112,10280,17476,43690,65536,
%T A277918 163840,278528,696320,1052672,2631680,4473856,11184640,16777472,
%U A277918 41943680,71304256,178260640,269488144,673720360,1145324612,2863311530,4294967296,10737418240
%N A277918 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 4", based on the 5-celled von Neumann neighborhood.
%C A277918 Initialized with a single black (ON) cell at stage zero.
%D A277918 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A277918 Robert Price, <a href="/A277918/b277918.txt">Table of n, a(n) for n = 0..126</a>
%H A277918 Robert Price, <a href="/A277918/a277918.tmp.txt">Diagrams of first 20 stages</a>
%H A277918 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 A277918 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A277918 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A277918 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A277918 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A277918 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A277918 CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
%t A277918 code=4; stages=128;
%t A277918 rule=IntegerDigits[code,2,10];
%t A277918 g=2*stages+1; (* Maximum size of grid *)
%t A277918 a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *)
%t A277918 ca=a;
%t A277918 ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}];
%t A277918 PrependTo[ca,a];
%t A277918 (* Trim full grid to reflect growth by one cell at each stage *)
%t A277918 k=(Length[ca[[1]]]+1)/2;
%t A277918 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 A277918 Table[FromDigits[Part[ca[[i]][[i]],Range[1,i]],2], {i,1,stages-1}]
%K A277918 nonn,easy
%O A277918 0,2
%A A277918 _Robert Price_, Nov 03 2016