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A273491
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 758", based on the 5-celled von Neumann neighborhood.
0
4, 4, 12, 12, 12, 16, 24, 44, 28, 32, 32, 60, 28, 48, 56, 76, 60, 64, 64, 92, 60, 80, 80, 108, 76, 96, 80, 124, 60, 112, 120, 140, 124, 128, 128, 156, 124, 144, 144, 172, 140, 160, 144, 188, 124, 176, 176, 204, 172, 192, 176, 220, 156, 208, 192, 236, 172
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=758; 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. A273486.
Sequence in context: A241496 A273412 A206488 * A168398 A281913 A178776
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 23 2016
STATUS
approved