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A169702
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First differences of A169701.
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2
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4, 3, 16, 1, 28, -17, 56, -4, 81, -97, 96, -20, 144, -136, 225, -85, 152, -88, 148, -12, 212, -279, 323, -8, 128, -171, 443, -255, 263, -183, 396, -209, 532, -419, 304, 107, 144, -132, 241, 47, 197, 11, 25, 299, 57, -37, 353, -237, 625, -224, 55, 169, 563, -599, 588, -81, 684, -627, 879, -552, 724
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history;
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OFFSET
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0,1
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COMMENTS
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First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 374", based on the 5-celled von Neumann neighborhood. 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=374; 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}];
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
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AUTHOR
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STATUS
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approved
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