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A270098
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Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 81", based on the 5-celled von Neumann neighborhood.
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4
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1, 4, 5, 40, 9, 100, 21, 196, 29, 320, 41, 476, 53, 640, 89, 844, 117, 1096, 129, 1380, 141, 1672, 177, 2004, 197, 2368, 217, 2764, 245, 3128, 321, 3532, 405, 4056, 369, 4652, 341, 5216, 349, 5824, 361, 6412, 429, 7032, 477, 7596, 561, 8324, 605, 9064, 593
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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=81; 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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