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A272556
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 497", based on the 5-celled von Neumann neighborhood.
4
1, 4, 13, 36, 37, 88, 85, 156, 109, 268, 181, 380, 237, 564, 365, 740, 317, 1028, 393, 1360, 393, 1500, 781, 1600, 861, 2060, 993, 2416, 1101, 2800, 1469, 3040, 1441, 3832, 1345, 4388, 1517, 4740, 1881, 5076, 2037, 5692, 2297, 6252, 2633, 6704, 2909, 7576
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=497; 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: A306349 A268996 A270988 * A173723 A002727 A320589
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 02 2016
STATUS
approved