That kind of regularity can still be explained in the language of commonly occurring sets: For a fractal, you reserve a symbol for the overall structure, which is common (in that something like it occurs frequently), and you have a symbol to instantiate it, given a particular position, to what scale. Time is handled similarly.

Yes but if you have a symbol for every possible fractal, it defeats the purpose. The point was to use time as a memory resource. This also works in reverse with caching and other methods, you can use memory as if it were time. Both, however, only work up to a point.