> What I mean is they all repeat in cycles that are called incommensurable — they are not likely to come back into sync again.

I remember a few years back there was some quick guide to visual design that I saw that recommended this. To provide what appeared to be randomness over repeating samples (or at least prevent easy pattern matching in the brain which is distracting), take three images that can of different prime number lengths, then repeat each one and put them next to each other.

I believe the example used was the ruffles in a stage curtain, where there were a few layers. Each layer was a repeating image of length 3, then length 5, then length 7 (but the image itself had some variations between ruffles within it). You won't get a point where all the images all stop and start at the same point (a dead giveaway of the pattern) until length 105.