Defining strict self-similarity

Question

I have been reading through John Hutchinson's paper "Fractals and Self-Similarity" and some other things, and I haven't really found a definition of strict self-similarity to work with that makes much sense to me. Heuristically we want (any?) part of a strictly self-similar object to look like a smaller copy of the whole object, but how to we formalise this so we can test (ask) whether some set is strictly self-similar?