A272730 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 517", based on the 5-celled von Neumann neighborhood.

1, 8, 20, 37, 60, 84, 129, 149, 224, 237, 329, 344, 473, 492, 624, 605, 844, 816, 969, 1024, 1288, 1249, 1405, 1545, 1800, 1800, 1937, 2096, 2520, 2433, 2596, 2748, 3165, 3164, 3260, 3565, 4016, 3981, 4004, 4504, 4869, 4788, 4960, 5477, 5825, 5853, 5888

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=517; 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: A004118 A082231 A318339 * A272738 A272782 A272805

Adjacent sequences: A272727 A272728 A272729 * A272731 A272732 A272733

Keyword

nonn,easy

Author

Robert Price, May 05 2016

Status

approved