A271543 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 387", based on the 5-celled von Neumann neighborhood.

1, 5, 9, 24, 17, 84, 41, 124, 57, 308, 65, 376, 141, 504, 125, 632, 149, 920, 285, 1052, 257, 1332, 281, 1564, 333, 1928, 489, 2040, 633, 2516, 617, 2624, 705, 3340, 701, 3580, 1017, 3872, 1029, 4636, 845, 5132, 1165, 5400, 1101, 6036, 1501, 6076, 1669, 7069

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=387; 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: A079993 A163607 A067294 * A272256 A132354 A146419

Adjacent sequences: A271540 A271541 A271542 * A271544 A271545 A271546

Keyword

nonn,easy,changed

Author

Robert Price, Apr 09 2016

Status

approved