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A273606
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 806", based on the 5-celled von Neumann neighborhood.
4
1, 5, 5, 17, 5, 25, 17, 61, 9, 45, 45, 125, 41, 157, 81, 213, 77, 169, 133, 337, 181, 401, 181, 413, 289, 505, 369, 569, 533, 657, 581, 829, 677, 793, 781, 1141, 837, 1033, 941, 1193, 1065, 1257, 1081, 1465, 1341, 1641, 1541, 1777, 1633, 1941, 1825, 2165
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=806; 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: A173464 A072272 A273502 * A273544 A273703 A253065
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 26 2016
STATUS
approved