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A265916
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 379", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 32, 21, 96, 41, 169, 44, 313, 100, 409, 80, 657, 128, 833, 152, 1057, 288, 1209, 220, 1737, 164, 1929, 441, 2196, 473, 2632, 397, 3104, 573, 3440, 617, 3952, 849, 4260, 753, 5000, 817, 5524, 985, 6028, 1133, 6656, 1033, 7360, 1357, 7784, 1389, 8761
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=379; 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: A271397 A264099 A271454 * A271889 A272447 A034435
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 09 2016
STATUS
approved