login
A273749
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 918", based on the 5-celled von Neumann neighborhood.
1
4, 4, 16, 4, 24, 0, 44, 4, 32, 24, 68, -12, 56, 0, 136, -12, 36, 68, 120, -48, 76, 40, 188, -44, 68, 44, 232, -44, 64, 56, 252, -40, 116, 84, 120, 56, 240, -60, 248, 60, 36, 104, 220, 40, 256, -48, 256, 76, 240, 68, 204, 124, 108, 164, 248, 32, 168, 64, 360
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=918; 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. A273746.
Sequence in context: A255302 A102376 A217954 * A273563 A278254 A091278
KEYWORD
sign,easy
AUTHOR
Robert Price, May 30 2016
STATUS
approved