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A273329
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 646", based on the 5-celled von Neumann neighborhood.
4
4, 0, 12, -8, 20, -12, 44, -44, 60, -44, 92, -80, 116, -92, 188, -196, 220, -196, 268, -256, 292, -268, 364, -364, 412, -364, 508, -472, 580, -508, 796, -828, 876, -828, 972, -960, 996, -972, 1068, -1068, 1116, -1068, 1212, -1176, 1284, -1212, 1500, -1524
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=646; 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. A273326.
Sequence in context: A273838 A273761 A273424 * A141554 A076600 A002978
KEYWORD
sign,easy
AUTHOR
Robert Price, May 20 2016
STATUS
approved