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A269698
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First differences of the numbers of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 6", based on the 5-celled von Neumann neighborhood.
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1
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4, -1, 16, -16, 16, -4, 64, -76, 16, -4, 64, -64, 64, -16, 256, -316, 16, -4, 64, -64, 64, -16, 256, -304, 64, -16, 256, -256, 256, -64, 1024, -1276, 16, -4, 64, -64, 64, -16, 256, -304, 64, -16, 256, -256, 256, -64, 1024, -1264, 64, -16, 256, -256, 256, -64
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OFFSET
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0,1
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COMMENTS
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Initialized with a single black (ON) cell at stage zero.
Rules 38, 70, 102, 134, 166, 198 and 230 also generate this sequence.
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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=6; 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 *)
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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