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A270188 First differences of 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. 1
4, 3, 16, 0, 24, -12, 72, -52, 56, -12, 132, -136, 108, -8, 240, -268, 208, -84, 324, -376, 244, -28, 336, -300, 356, -88, 220, -216, 140, 104, 360, -348, 492, -252, 528, -636, 436, 160, 272, -364, 472, -96, 364, -516, 404, 144, 644, -784, 660, 320, -348 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
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}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)
CROSSREFS
Cf. A270185.
Sequence in context: A324013 A345013 A113204 * A010309 A169702 A272422
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 12 2016
STATUS
approved

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Last modified April 19 12:14 EDT 2024. Contains 371792 sequences. (Running on oeis4.)