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A270930
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Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 219", based on the 5-celled von Neumann neighborhood.
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4
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1, 5, 5, 37, 8, 97, 25, 185, 33, 329, 48, 461, 64, 641, 117, 817, 109, 1133, 157, 1365, 161, 1641, 225, 1881, 256, 2357, 333, 2753, 421, 3189, 445, 3473, 497, 4049, 505, 4641, 541, 5097, 684, 5661, 716, 6385, 776, 6937, 964, 7621, 976, 8217, 1072, 8901, 1096
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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=219; 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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