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A273119
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 593", based on the 5-celled von Neumann neighborhood.
4
1, 4, 17, 25, 60, 65, 137, 136, 224, 221, 345, 328, 476, 469, 641, 664, 796, 849, 1001, 1068, 1220, 1285, 1493, 1524, 1736, 1797, 2045, 2096, 2336, 2429, 2661, 2824, 3048, 3193, 3356, 3636, 3925, 3953, 4408, 4396, 4865, 4837, 5316, 5352, 5769, 5865, 6288
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=593; 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: A192197 A009226 A273022 * A302618 A171227 A061387
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 15 2016
STATUS
approved