A272506 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 486", based on the 5-celled von Neumann neighborhood.

1, 5, 4, 20, 9, 37, 28, 57, 41, 72, 101, 152, 148, 204, 244, 332, 281, 317, 288, 368, 448, 493, 556, 712, 709, 728, 793, 876, 925, 960, 1045, 1328, 1273, 1269, 1257, 1437, 1429, 1605, 1753, 1921, 1997, 1993, 2153, 2325, 2361, 2349, 2608, 2969, 2860, 2729

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=486; 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: A271259 A271409 A246326 * A070374 A057423 A327317

Adjacent sequences: A272503 A272504 A272505 * A272507 A272508 A272509

Keyword

nonn,easy

Author

Robert Price, May 01 2016

Status

approved