login
A270988
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 241", based on the 5-celled von Neumann neighborhood.
4
1, 4, 13, 36, 37, 88, 77, 156, 113, 284, 121, 432, 229, 560, 337, 736, 305, 1072, 361, 1188, 601, 1452, 677, 1768, 853, 2144, 765, 2500, 1121, 2828, 1237, 3132, 1269, 3836, 1221, 4080, 1785, 4552, 1644, 5164, 2045, 5592, 2228, 6304, 2477, 6684, 2913, 7224
OFFSET
0,2
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=241; 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}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
CROSSREFS
Sequence in context: A271358 A306349 A268996 * A272556 A173723 A002727
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 27 2016
STATUS
approved