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A270185 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 118", based on the 5-celled von Neumann neighborhood. 4
1, 5, 8, 24, 24, 48, 36, 108, 56, 112, 100, 232, 96, 204, 196, 436, 168, 376, 292, 616, 240, 484, 456, 792, 492, 848, 760, 980, 764, 904, 1008, 1368, 1020, 1512, 1260, 1788, 1152, 1588, 1748, 2020, 1656, 2128, 2032, 2396, 1880, 2284, 2428, 3072, 2288, 2948 (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=118; 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: A264797 A270905 A253078 * A169701 A271008 A272577
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 12 2016
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)