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A273204
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 606", based on the 5-celled von Neumann neighborhood.
4
1, 5, 13, 21, 33, 37, 77, 81, 81, 113, 169, 177, 165, 205, 313, 297, 301, 321, 505, 421, 485, 477, 737, 589, 693, 677, 961, 805, 945, 921, 1253, 1037, 1241, 1201, 1577, 1349, 1557, 1505, 1901, 1673, 1829, 1801, 2225, 2041, 2169, 2293, 2613, 2477, 2521, 2685
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=606; 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: A288418 A034170 A272809 * A273392 A273453 A299770
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 17 2016
STATUS
approved