A271461 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 377", based on the 5-celled von Neumann neighborhood.

1, 4, 9, 32, 17, 104, 29, 180, 61, 312, 73, 460, 121, 652, 137, 860, 169, 1076, 261, 1308, 293, 1648, 341, 1980, 349, 2300, 513, 2604, 561, 3088, 565, 3592, 661, 3896, 873, 4412, 809, 4944, 905, 5548, 965, 6112, 1101, 6664, 1265, 7292, 1373, 8128, 1285, 8728

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=377; 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: A270177 A268277 A270206 * A272423 A280163 A361987

Adjacent sequences: A271458 A271459 A271460 * A271462 A271463 A271464

Keyword

nonn,easy

Author

Robert Price, Apr 08 2016

Status

approved