login
A273249
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 617", based on the 5-celled von Neumann neighborhood.
1
3, 17, 8, 43, 16, 64, 0, 112, 24, 112, 16, 160, 8, 184, -72, 288, 16, 264, 16, 240, 24, 328, -72, 424, -56, 432, -104, 504, -192, 608, -408, 768, -128, 664, -144, 616, -168, 800, -120, 700, -136, 724, -184, 888, -256, 868, -576, 1292, -352, 1004, -512, 1280
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=617; 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. A273246.
Sequence in context: A093844 A273211 A273273 * A273303 A362086 A033467
KEYWORD
sign,easy
AUTHOR
Robert Price, May 18 2016
STATUS
approved