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%I A283223 #32 Mar 04 2017 08:39:28
%S A283223 1,1,1,101,101,10101,10001,1011101,1001001,101111101,100101001,
%T A283223 10111111101,10011111001,1011111111101,1001010101001,101111111011101,
%U A283223 100111110001001,10111111101111101,10010101000111001,1011111111111010101,1001111101110000101
%N A283223 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 603", based on the 5-celled von Neumann neighborhood.
%C A283223 Initialized with a single black (ON) cell at stage zero.
%D A283223 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A283223 Robert Price, <a href="/A283223/b283223.txt">Table of n, a(n) for n = 0..126</a>
%H A283223 Robert Price, <a href="/A283223/a283223.tmp.txt">Diagrams of first 20 stages</a>
%H A283223 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 A283223 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A283223 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A283223 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A283223 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A283223 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A283223 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A283223 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A283223 code = 603; stages = 128;
%t A283223 rule = IntegerDigits[code, 2, 10];
%t A283223 g = 2 * stages + 1; (* Maximum size of grid *)
%t A283223 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A283223 ca = a;
%t A283223 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A283223 PrependTo[ca, a];
%t A283223 (* Trim full grid to reflect growth by one cell at each stage *)
%t A283223 k = (Length[ca[[1]]] + 1)/2;
%t A283223 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 A283223 Table[FromDigits[Part[ca[[i]] [[i]], Range[1, i]], 10], {i, 1, stages - 1}]
%Y A283223 Cf. A283249, A283250, A283251.
%K A283223 nonn,easy
%O A283223 0,4
%A A283223 _Robert Price_, Mar 03 2017

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