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A272742
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 526", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 17, 17, 33, 45, 69, 61, 85, 97, 121, 121, 169, 205, 277, 245, 293, 305, 329, 329, 377, 413, 485, 461, 533, 569, 641, 641, 785, 893, 1109, 1005, 1125, 1137, 1161, 1161, 1209, 1245, 1317, 1293, 1365, 1401, 1473, 1473, 1617, 1725, 1941, 1845, 1989
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=526; 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: A215331 A208725 A362108 * A273534 A273115 A273687
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 05 2016
STATUS
approved

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Last modified September 20 12:37 EDT 2024. Contains 376072 sequences. (Running on oeis4.)