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A272730
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 517", based on the 5-celled von Neumann neighborhood.
4
1, 8, 20, 37, 60, 84, 129, 149, 224, 237, 329, 344, 473, 492, 624, 605, 844, 816, 969, 1024, 1288, 1249, 1405, 1545, 1800, 1800, 1937, 2096, 2520, 2433, 2596, 2748, 3165, 3164, 3260, 3565, 4016, 3981, 4004, 4504, 4869, 4788, 4960, 5477, 5825, 5853, 5888
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=517; 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: A004118 A082231 A318339 * A272738 A272782 A272805
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 05 2016
STATUS
approved