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A273765
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 910", based on the 5-celled von Neumann neighborhood.
1
4, 4, 8, 4, 8, 8, 32, 20, -4, 4, 64, 48, -4, 28, 68, 28, -20, -8, 96, 36, -84, 40, 116, 8, -8, 44, 176, 68, -40, 68, 176, 76, -96, 24, 208, 24, -148, 0, 32, 140, 24, 12, 152, 100, 40, 92, 160, 128, -108, 104, 376, -80, -144, 208, 204, 116, -52, -20, 404, 264
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=910; 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. A273762.
Sequence in context: A167275 A273333 A273428 * A273854 A082075 A243641
KEYWORD
sign,easy
AUTHOR
Robert Price, May 29 2016
STATUS
approved