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A270177
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 113", based on the 5-celled von Neumann neighborhood.
4
1, 4, 9, 32, 17, 88, 37, 184, 44, 297, 92, 429, 112, 629, 100, 845, 140, 1009, 224, 1324, 225, 1632, 244, 1897, 380, 2221, 328, 2597, 464, 3021, 532, 3445, 560, 3837, 648, 4417, 792, 4845, 756, 5485, 940, 5953, 1044, 6717, 1020, 7169, 1292, 7777, 1468, 8561
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=113; 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: A271305 A270160 A271414 * A268277 A270206 A271461
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 12 2016
STATUS
approved