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A273215
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 611", based on the 5-celled von Neumann neighborhood.
1
4, 12, 20, 24, 36, 36, 40, 36, 128, 60, 64, 68, 92, 60, 76, 64, 296, 92, 168, 92, 184, 112, 100, 96, 332, 108, 192, 104, 200, 128, 172, 80, 684, 60, 460, 132, 296, 300, 196, 180, 436, 116, 252, 280, 320, 248, 112, 224, 780, 204, 380, 336, 380, 244, 368, 16
OFFSET
0,1
COMMENTS
Initialized with a single black (ON) cell at stage zero.
The first negative term is a(65) = -28. - Georg Fischer, Feb 15 2019
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=611; 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. A273212.
Sequence in context: A050426 A061820 A273541 * A273277 A100717 A365883
KEYWORD
sign,easy
AUTHOR
Robert Price, May 17 2016
STATUS
approved