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A270125
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 86", based on the 5-celled von Neumann neighborhood.
4
1, 5, 8, 24, 16, 48, 32, 96, 32, 96, 64, 192, 64, 192, 128, 384, 64, 192, 128, 384, 128, 384, 256, 768, 128, 384, 256, 768, 256, 768, 512, 1536, 128, 384, 256, 768, 256, 768, 512, 1536, 256, 768, 512, 1536, 512, 1536, 1024, 3072, 256, 768, 512, 1536, 512
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=86; 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: A116884 A192651 A105963 * A264797 A270905 A253078
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 11 2016
STATUS
approved