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A272804 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 539", based on the 5-celled von Neumann neighborhood. 1
4, 8, 16, 20, 40, 16, 68, 12, 116, -12, 132, 4, 128, 20, 152, 36, 204, -48, 312, -68, 300, -92, 360, -112, 468, -184, 476, -224, 604, -240, 536, -68, 504, -180, 644, -156, 512, -172, 736, -288, 668, -236, 820, -196, 432, 284, 396, 44, 476, 44, 860, -188, 556 (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=539; 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. A272801.
Sequence in context: A036693 A181471 A272753 * A237990 A335792 A312807
KEYWORD
sign,easy
AUTHOR
Robert Price, May 06 2016
STATUS
approved

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Last modified May 22 17:00 EDT 2024. Contains 372758 sequences. (Running on oeis4.)