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A268276 - OEIS
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A268276
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 366", based on the 5-celled von Neumann neighborhood.
1
4, 3, 13, 3, 13, 15, 25, 11, 21, -1, 33, 35, 21, 31, 97, -37, 40, 45, -45, 52, 65, 7, 96, -44, 80, 109, -9, 65, 135, 113, 227, -27, -101, 161, -129, 124, 52, -47, 203, 37, -81, 152, 89, -13, 64, 265, -125, 316, -31, 243, -288, 477, -233, 432, 29, 55, 284
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=366; 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. A268195.
Sequence in context: A272312 A272117 A271159 * A169706 A355933 A370924
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 07 2016
STATUS
approved