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A273077
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 587", based on the 5-celled von Neumann neighborhood.
4
1, 5, 13, 29, 57, 73, 121, 141, 209, 241, 297, 329, 469, 501, 613, 633, 781, 837, 905, 1029, 1177, 1257, 1485, 1441, 1673, 1825, 1905, 2109, 2293, 2413, 2593, 2769, 3001, 3021, 3377, 3401, 3813, 3729, 4157, 4325, 4561, 4689, 4881, 5229, 5509, 5561, 6021
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=587; 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: A299895 A307674 A273026 * A160430 A347503 A023617
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 14 2016
STATUS
approved