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A272790
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Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 537", based on the 5-celled von Neumann neighborhood.
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4
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1, 4, 13, 28, 49, 81, 88, 173, 193, 253, 248, 397, 408, 533, 512, 741, 749, 897, 857, 1152, 1176, 1325, 1289, 1721, 1549, 1960, 1825, 2197, 2220, 2573, 2316, 2993, 2936, 3293, 3048, 3781, 3656, 4252, 3969, 4733, 4437, 5157, 4785, 5680, 5313, 6165, 5753, 6661
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OFFSET
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0,2
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COMMENTS
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Initialized with a single black (ON) cell at stage zero.
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
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LINKS
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MATHEMATICA
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CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=537; stages=128;
rule=IntegerDigits[code, 2, 10];
g=2*stages+1; (* Maximum size of grid *)
a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca=a;
ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k=(Length[ca[[1]]]+1)/2;
ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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