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A271414
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 361", based on the 5-celled von Neumann neighborhood.
3
1, 4, 9, 32, 13, 92, 45, 160, 37, 300, 69, 416, 53, 628, 173, 736, 133, 1040, 137, 1272, 193, 1612, 345, 1832, 313, 2284, 365, 2556, 417, 3012, 597, 3300, 509, 3912, 561, 4360, 553, 4864, 741, 5516, 765, 6008, 849, 6504, 853, 7184, 1229, 7608, 1053, 8472
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=361; 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: A270152 A271305 A270160 * A270177 A268277 A270206
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 06 2016
STATUS
approved