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A270720
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 201", based on the 5-celled von Neumann neighborhood.
4
1, 4, 9, 28, 17, 80, 28, 133, 64, 241, 72, 348, 109, 532, 137, 656, 212, 865, 204, 1049, 296, 1349, 304, 1557, 432, 1781, 496, 2085, 632, 2421, 720, 2705, 744, 3105, 912, 3504, 849, 4032, 1160, 4349, 1128, 4904, 1233, 5228, 1361, 5848, 1480, 6237, 1660, 6825
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=201; 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: A007872 A272016 A272089 * A272280 A087726 A270891
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 22 2016
STATUS
approved