A272330 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 601", based on the 5-celled von Neumann neighborhood.

1, 4, 17, 29, 61, 73, 132, 148, 244, 224, 357, 349, 505, 461, 705, 645, 956, 816, 1144, 996, 1413, 1205, 1749, 1477, 2057, 1717, 2389, 2097, 2764, 2364, 3225, 2781, 3669, 3029, 4116, 3408, 4605, 3833, 5129, 4329, 5717, 4725, 6257, 5241, 6792, 5708, 7529

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.

Links

Robert Price, Table of n, a(n) for n = 0..128

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to 2D 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

Robert Price, Diagrams of the first 20 stages

Mathematica

CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=601; 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: A272991 A273430 A273073 * A163736 A249582 A127547

Adjacent sequences: A272327 A272328 A272329 * A272331 A272332 A272333

Keyword

nonn,easy

Author

Robert Price, May 17 2016

Status

approved