A271200 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 313", based on the 5-celled von Neumann neighborhood.

1, 4, 5, 32, 13, 88, 21, 168, 37, 284, 77, 444, 73, 620, 109, 804, 181, 1008, 173, 1328, 221, 1588, 289, 1948, 281, 2292, 397, 2656, 381, 3036, 481, 3552, 509, 3984, 649, 4440, 721, 5028, 777, 5556, 797, 6144, 865, 6768, 897, 7368, 1141, 8068, 1205, 8640

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

Robert Price, Diagrams of the first 20 stages.

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

Mathematica

CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=313; 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: A269872 A270075 A271148 * A335526 A262711 A215614

Adjacent sequences: A271197 A271198 A271199 * A271201 A271202 A271203

Keyword

nonn,easy

Author

Robert Price, Apr 01 2016

Status

approved