below, is that some process can start at one point in space and then progressively spread, doing the same thing at every point it reaches.
Another mechanism is that every part of a system can evolve completely independently to the same state, as in the pictures below.
A slightly less straightforward mechanism is illustrated in the pictures below. Here different elements in the system do interact, but the result is still that all of them evolve to the same state.
So far all the mechanisms for uniformity I have mentioned involve behavior that is in a sense simple at every level. But in nature uniformity often seems to be associated with quite complex microscopic behavior. Most often what happens is that on a small scale a system exhibits randomness, but on a larger scale this randomness averages out to leave apparent uniformity, as in the pictures below.