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A273795
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 934", based on the 5-celled von Neumann neighborhood.
1
4, 0, 12, -8, 20, -8, 44, -32, 28, -16, 76, -48, 64, -56, 148, -76, 100, -68, 156, -84, 156, -28, 196, -52, 144, -48, 220, -88, 180, -40, 320, -100, 68, -16, 316, -60, 200, -24, 248, -32, 208, -40, 340, -96, 280, -16, 336, -84, 216, 40, 376, -68, 292, 32
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=934; 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. A273792.
Sequence in context: A174087 A072194 A225952 * A273858 A273485 A151921
KEYWORD
sign,easy
AUTHOR
Robert Price, May 30 2016
STATUS
approved