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A273392
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 670", based on the 5-celled von Neumann neighborhood.
4
1, 5, 13, 21, 33, 49, 61, 81, 105, 117, 149, 157, 225, 253, 325, 293, 449, 445, 545, 501, 673, 589, 777, 677, 881, 941, 1017, 925, 1209, 1093, 1345, 1237, 1545, 1621, 1673, 1765, 1985, 1885, 2257, 2093, 2409, 2501, 2521, 2557, 2945, 2749, 3225, 3061, 3385
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=670; 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: A034170 A272809 A273204 * A273453 A299770 A294962
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 21 2016
STATUS
approved