login
A272315
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 467", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 28, 29, 80, 53, 136, 117, 232, 141, 352, 205, 496, 253, 608, 421, 808, 397, 1112, 389, 1444, 497, 1572, 801, 1868, 761, 2240, 849, 2584, 989, 2720, 1525, 3056, 1325, 3792, 1309, 4336, 1465, 4804, 1549, 5448, 1585, 5980, 1897, 6460, 2105, 6776, 2657
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=467; 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: A271685 A271807 A272287 * A301747 A193316 A026587
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 25 2016
STATUS
approved