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A272423
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 473", based on the 5-celled von Neumann neighborhood.
4
1, 4, 9, 32, 21, 100, 41, 164, 73, 296, 101, 436, 137, 624, 197, 724, 301, 1008, 265, 1340, 329, 1660, 337, 1880, 469, 2300, 577, 2652, 681, 3088, 749, 3216, 1117, 3788, 1017, 4364, 1153, 5100, 961, 5540, 1249, 6052, 1497, 6624, 1653, 7356, 1705, 7652, 2161
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=473; 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: A268277 A270206 A271461 * A280163 A361987 A071378
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 29 2016
STATUS
approved