I thoroughly enjoyed reading that. You have convinced me. I always like entertaining my imagination with the concept of infinite fractals since my first fractal 25 yrs ago – yet something kept me from believing it was anything but a fascinating side effect of graphing particular formulas a certain way that resulted in self similar patterns. They make a nice analogy to some real world systems in a rough way but upon stricter analysis the fractals disappear.
That being said, I will continue my lifelong on and off fascination with fractals and some of their properties. I have a general “rule of thumb” that for each place that there is a gap, you will find another gap within that gap, and so on. There is a point (not literally a point) where things “stop” but until then, a “gaps within gaps within gaps within gaps” is a useful way for me to visualize reality from the macro to the micro as it were. Cracks within cracks. It does have an end, just like a fracture ends with the material yet it can produce some interesting effects until that point in time…. well space.. well.. not space either… and not really a point at all… but I think you know what I mean.