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A273029
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 579", based on the 5-celled von Neumann neighborhood.
1
4, 8, 16, 28, 16, 48, 12, 76, 4, 88, 36, 96, 16, 176, -48, 200, -8, 128, 104, 160, -24, 376, -128, 260, 128, 72, 172, 236, -52, 500, -132, 296, 12, 392, 20, 224, 256, 336, -132, 620, -60, 264, 172, 456, 132, 232, 216, 300, 268, 440, -164, 608, 180, 576, -272
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=579; 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. A273026.
Sequence in context: A334198 A358730 A303544 * A273080 A020193 A176817
KEYWORD
sign,easy
AUTHOR
Robert Price, May 13 2016
STATUS
approved