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A272920
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 555", based on the 5-celled von Neumann neighborhood.
4
1, 5, 17, 29, 61, 89, 129, 149, 221, 281, 353, 405, 501, 569, 657, 669, 829, 953, 1089, 1205, 1365, 1497, 1649, 1725, 1941, 2105, 2289, 2397, 2621, 2745, 2913, 2837, 3197, 3449, 3713, 3957, 4245, 4505, 4785, 4989, 5333, 5625, 5937, 6173, 6525, 6777, 7073
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=555; 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: A246334 A272838 A272939 * A143798 A031013 A031370
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 10 2016
STATUS
approved