Layers work well.
Here's some maths:
Suppose you have a railway track that's been poorly made such that the like
__ __ notice the gap between them. When the wheel rolls over them it makes a small notch (tiny notch).
If the track length is
l and the wheel has radius
2pi r is the circumfrence of the wheel,
ration=l/(2pi r) if the ratio is say 10.25 then the wheel will get a notch in it every quarter as it rides a long.
This is the easiest way I can think of to explain covering spaces.
So suppose you have two images, if one has this quarter ratio you'll get a 4-phase pattern, it'll repeat after 4 tiles. Suppose you have 1 main background and 2 overlays, with m and n phases. Then the pattern will repeat after m*n tiles.
While it wont matter much the pattern will look best if the numbers are co-prime, that is the greatest common divisor is 1. For example suppose we have something of phase 6 and something of phase 4, every other phase these will "line up" in a sense.
You can use this technique (especially with particles and stuff) to create a lot of "unique" stuff with very little effort.
Back to the train wheel, if the ratio is irrational, then the notches will cover the the wheel! But this doesn't really matter.