login
A271160
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 305", based on the 5-celled von Neumann neighborhood.
4
1, 4, 5, 32, 9, 100, 21, 200, 33, 316, 49, 448, 69, 624, 81, 860, 101, 1060, 141, 1324, 185, 1632, 209, 1944, 245, 2264, 269, 2620, 325, 3004, 389, 3448, 461, 3864, 469, 4420, 485, 4856, 585, 5392, 737, 6064, 705, 6596, 713, 7296, 841, 7936, 925, 8544, 969
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=305; 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: A269810 A271125 A270014 * A269872 A270075 A271148
KEYWORD
nonn,easy,changed
AUTHOR
Robert Price, Mar 31 2016
STATUS
approved