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A273277
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 627", based on the 5-celled von Neumann neighborhood.
1
4, 12, 20, 24, 40, 20, 52, 44, 108, 12, 104, 56, 112, 48, 128, 24, 232, 80, 124, 112, 228, 56, 112, 84, 252, 204, 124, 200, 200, 148, 172, 160, 344, 292, 248, 260, 280, 104, 388, 60, 340, 328, 256, 288, 120, 496, 288, 84, 612, 196, 420, 308, 380, 176, 332
OFFSET
0,1
COMMENTS
Initialized with a single black (ON) cell at stage zero.
First negative terms is a(115) = -8. - 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=627; 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. A273274.
Sequence in context: A061820 A273541 A273215 * A100717 A365883 A285526
KEYWORD
sign,easy
AUTHOR
Robert Price, May 18 2016
STATUS
approved