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A272991 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 569", based on the 5-celled von Neumann neighborhood. 4
1, 4, 17, 28, 61, 93, 133, 149, 213, 297, 353, 413, 497, 577, 685, 665, 781, 1029, 1093, 1245, 1381, 1473, 1701, 1757, 1929, 2189, 2281, 2417, 2633, 2741, 2941, 2965, 3153, 3649, 3757, 4177, 4377, 4553, 4977, 5113, 5377, 5693, 5901, 6145, 6653, 6773, 7081 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=569; 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: A273610 A272769 A273646 * A273430 A273073 A272330
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 12 2016
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)