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A272702
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 513", based on the 5-celled von Neumann neighborhood.
4
1, 4, 13, 24, 53, 65, 113, 112, 229, 241, 321, 289, 505, 489, 601, 480, 965, 977, 1121, 1025, 1433, 1353, 1529, 1217, 2153, 2105, 2313, 2033, 2753, 2489, 2729, 1984, 3973, 3985, 4257, 4033, 4825, 4617, 4921, 4225, 6057, 5881, 6217, 5553, 6913, 6265, 6633
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=513; 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: A085018 A255840 A001741 * A272734 A273414 A154820
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 04 2016
STATUS
approved