login
A272838
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 547", based on the 5-celled von Neumann neighborhood.
4
1, 5, 17, 29, 61, 89, 121, 149, 213, 273, 337, 397, 477, 537, 601, 661, 789, 913, 1041, 1165, 1309, 1433, 1561, 1685, 1861, 2017, 2169, 2309, 2453, 2537, 2633, 2757, 3013, 3265, 3521, 3773, 4045, 4297, 4553, 4805, 5109, 5393, 5673, 5941, 6213, 6425, 6649
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=547; 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: A091851 A079292 A246334 * A272939 A272920 A143798
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 07 2016
STATUS
approved