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A269810
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Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 33", based on the 5-celled von Neumann neighborhood.
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4
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1, 4, 5, 32, 9, 92, 21, 164, 25, 288, 37, 420, 57, 572, 85, 732, 89, 984, 101, 1244, 121, 1520, 165, 1772, 209, 2084, 269, 2412, 281, 2748, 349, 3084, 353, 3592, 365, 4108, 385, 4640, 429, 5148, 473, 5712, 549, 6260, 601, 6784, 741, 7308, 753, 7940, 877
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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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rule=33; stages=300;
ca=CellularAutomaton[{rule, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, stages]; (* Start with single black cell *)
l=Length[ca[[1]]]; k=(l+1)/2; s=stages; (* Limit scope to one cell growth per stage *)
ca=Table[Table[Part[ca[[n]][[j]], Range[Max[1, k+1-n], Min[l, k-1+n]]], {j, Max[1, k+1-n], Min[l, k-1+n]}], {n, 1, s+1}];
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,changed
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AUTHOR
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STATUS
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approved
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