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A273299
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 633", based on the 5-celled von Neumann neighborhood.
8
1, 4, 21, 29, 72, 88, 156, 160, 269, 269, 396, 420, 580, 572, 784, 736, 1008, 968, 1316, 1348, 1572, 1532, 1896, 1796, 2213, 2157, 2621, 2525, 3017, 2817, 3413, 3173, 3881, 3625, 4545, 4273, 5033, 4785, 5537, 5209, 6089, 5833, 6701, 6349, 7389, 6941, 7953
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=633; 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: A273208 A273270 A273246 * A306285 A273699 A273707
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 19 2016
STATUS
approved