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A272049
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 421", based on the 5-celled von Neumann neighborhood.
4
1, 8, 5, 40, 17, 108, 29, 180, 65, 324, 61, 460, 113, 676, 101, 788, 225, 1092, 185, 1384, 249, 1656, 237, 1864, 377, 2288, 317, 2660, 469, 3064, 469, 3372, 669, 3980, 577, 4480, 681, 5072, 761, 5500, 725, 6124, 881, 6720, 1065, 7428, 1097, 7796, 1417, 8748
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=421; 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: A213841 A271594 A272273 * A272350 A271812 A272416
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 18 2016
STATUS
approved