Comment by nwjtkjn

Good point, though I'm not convinced Hilbert really avoids this. For example, look at n=3 here:

http://www.texample.net/media/tikz/examples/PNG/hilbert-curv...

This might lead to say

. . . . . . . .

1 . . . . . . 2

4 . . . . . . 3

. . . . . . . .

when

. . . . . . . .

1 . . . . . . 4

2 . . . . . . 3

. . . . . . . .

is more efficient.

Generally speaking, it seems this is basically TSP.