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A273073
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 585", based on the 5-celled von Neumann neighborhood.
4
1, 4, 17, 29, 49, 81, 133, 125, 176, 249, 301, 337, 401, 485, 585, 609, 709, 785, 897, 993, 1141, 1297, 1437, 1509, 1685, 1725, 1897, 1909, 2201, 2429, 2645, 2521, 2792, 2929, 3261, 3188, 3493, 3701, 4121, 4109, 4377, 4493, 5001, 5065, 5165, 5589, 5916, 5793
OFFSET
0,2
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=585; 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 *)
CROSSREFS
Sequence in context: A273646 A272991 A273430 * A272330 A163736 A249582
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 14 2016
STATUS
approved