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A272994
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 569", based on the 5-celled von Neumann neighborhood.
1
3, 13, 11, 33, 32, 40, 16, 64, 84, 56, 60, 84, 80, 108, -20, 116, 248, 64, 152, 136, 92, 228, 56, 172, 260, 92, 136, 216, 108, 200, 24, 188, 496, 108, 420, 200, 176, 424, 136, 264, 316, 208, 244, 508, 120, 308, 24, 320, 680, -72, 608, 228, 432, 336, 76, 360
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.
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=569; 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. A272991.
Sequence in context: A212552 A272938 A273649 * A273674 A360967 A214811
KEYWORD
sign,easy,changed
AUTHOR
Robert Price, May 12 2016
STATUS
approved