Fractal theories of self-similarity cover an interme-diate size range around the human-size level (such as sea coasts and clouds), but self-similarity peters out (or ends abruptly?) at very small (quantum realm) sizes and very large (relativistic realm) sizes, where very different phe-nomena and theories take over.

This means that the applicability range of self-similarity is not infinite, as perhaps suggested (at the micro end) by such images as mirrors within mirrors, Russian dolls, Chinese boxes, and Hofstadter’s Djinns (in “Escher, Godel, Bach”). This is analogous to theories of atoms and light quanta – matter and light are not infinitely divisible (continuous), but hit a lower limit of “phase change” when something else starts happening. Fractality is like that too, and even space-time may be (there are theories of space tearing apart or becoming “bubbly” at extremely small dimen-sions). However, not numbers – these are truly continuous: the irrationals densely fill all interstices between fractions – a truly fractal array without lower limit. Perhaps matter and energy configurations are necessarily discon-tinuous, but mental constructions need not be.