A271148 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 297", based on the 5-celled von Neumann neighborhood.

1, 4, 5, 32, 13, 88, 17, 168, 33, 276, 29, 432, 81, 580, 41, 800, 125, 968, 53, 1344, 141, 1560, 89, 1888, 241, 2100, 117, 2640, 281, 2892, 205, 3352, 413, 3704, 229, 4348, 437, 4632, 317, 5284, 549, 5644, 369, 6424, 737, 6816, 373, 7884, 649, 8172, 633

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=297; 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: A271160 A269872 A270075 * A271200 A335526 A373190

Adjacent sequences: A271145 A271146 A271147 * A271149 A271150 A271151

Keyword

nonn,easy

Author

Robert Price, Mar 31 2016

Status

approved