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A273706
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 870", based on the 5-celled von Neumann neighborhood.
1
4, 0, 12, -12, 20, -8, 44, -52, 36, 0, 84, -72, 84, -24, 168, -164, 88, 8, 100, -52, 128, 4, 228, -124, 60, 56, 180, -100, 184, -36, 252, -164, 132, 76, 128, -172, 228, 36, 252, -72, 136, -4, 236, 36, 360, -164, 216, -212, 180, 40, 356, -292, 228, -28, 564
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=870; 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. A273703.
Sequence in context: A002978 A273609 A273505 * A273682 A170878 A056460
KEYWORD
sign,easy
AUTHOR
Robert Price, May 28 2016
STATUS
approved