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A272279
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 454", based on the 5-celled von Neumann neighborhood.
1
4, -1, 16, -11, 28, -9, 29, -28, 43, 0, 73, -48, 68, -8, 76, -92, 108, -44, 84, -20, 164, -5, 76, -167, 151, -40, 261, -148, 144, 3, 272, -247, 163, -4, 32, -48, 265, -5, 236, -140, 141, -157, 412, -115, 344, -220, 355, -308, 452, -47, 171, -92, 260, 77, 195
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=454; 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. A246326.
Sequence in context: A271601 A271068 A272509 * A271413 A271262 A292922
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 24 2016
STATUS
approved