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A273541
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 779", based on the 5-celled von Neumann neighborhood.
1
4, 12, 20, 24, 36, 28, 72, 40, 68, 32, 136, 48, 96, 12, 272, 72, 132, 32, 264, 48, 160, -48, 528, 80, 192, -16, 440, 0, 216, -212, 1056, 136, 260, 32, 520, 48, 288, -176, 1040, 80, 320, -144, 824, -128, 344, -592, 2080, 144, 384, -80, 888, -64, 408, -528
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=779; 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. A273538.
Sequence in context: A104814 A050426 A061820 * A273215 A273277 A100717
KEYWORD
sign,easy,changed
AUTHOR
Robert Price, May 24 2016
STATUS
approved