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A270136
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 94", based on the 5-celled von Neumann neighborhood.
1
4, 7, 4, 20, -12, 36, -16, 72, -64, 96, -52, 148, -168, 152, -48, 240, -300, 188, -76, 324, -308, 300, -180, 444, -504, 248, -8, 388, -296, 192, 4, 340, -292, 4, 60, 552, -408, 244, 32, 496, -632, 352, 108, 444, -368, 144, 72, 692, -848, 344, 256, 512, -476
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=94; 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. A270133.
Sequence in context: A106027 A101159 A339948 * A269756 A166530 A011518
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 11 2016
STATUS
approved