I wonder if there are any 3d space-filling curves that "make sense" for this type of analysis. You somehow have to wrap points around (0,0,0) in a way that has nice properties like the spiral. For instance, zig-zagging around a 3d box [1] Probably has too many 2d "artifacts" (I'm not a mathematician).

The 2d spiral has these really nice properties that contiguous numbers are adjacent, it is approximately symmetric for any rotation in R2, and each number is only +ε farther away from the origin.

[1]http://vgalt.com/wp-content/uploads/2009/10/3d-labyrinth.jpg