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A273118
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 590", based on the 5-celled von Neumann neighborhood.
1
4, 4, 8, 0, 20, 12, -8, 16, 20, 20, 16, 28, 8, 76, -36, 60, 0, 112, -104, 92, 60, 28, 92, -4, 12, 100, 44, 4, 148, 20, 124, 96, -116, 176, -56, 56, 120, -60, 200, 12, 64, 68, 184, 72, 160, -4, 256, -220, 240, 140, -32, 40, 320, -124, 268, -4, 52, 228, 16
OFFSET
0,1
COMMENTS
Initialized with a single black (ON) cell at stage zero.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=590; 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 *)
CROSSREFS
Cf. A273115.
Sequence in context: A298815 A272745 A273537 * A273690 A010660 A372765
KEYWORD
sign,easy
AUTHOR
Robert Price, May 15 2016
STATUS
approved