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A268277
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 369", based on the 5-celled von Neumann neighborhood.
4
1, 4, 9, 32, 17, 92, 37, 176, 61, 300, 69, 436, 137, 580, 153, 844, 161, 1028, 253, 1284, 273, 1620, 329, 1924, 413, 2304, 489, 2616, 529, 3040, 621, 3432, 649, 4004, 773, 4364, 845, 4892, 1061, 5376, 989, 6096, 1105, 6688, 1141, 7404, 1165, 7928, 1537, 8500
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=369; 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: A270160 A271414 A270177 * A270206 A271461 A272423
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 07 2016
STATUS
approved