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A272746
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 529", based on the 5-celled von Neumann neighborhood.
4
1, 4, 13, 28, 49, 77, 96, 149, 180, 257, 256, 373, 388, 513, 476, 709, 692, 857, 828, 1129, 1032, 1301, 1224, 1605, 1584, 1789, 1812, 2149, 2132, 2445, 2368, 2861, 2684, 3121, 3100, 3461, 3544, 3785, 3848, 4341, 4284, 4817, 4772, 5237, 5292, 5697, 5784, 6085
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=529; 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: A307272 A056107 A155433 * A273557 A272790 A273564
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 05 2016
STATUS
approved