Can a point that is unmeasurable ever exist? The existence of this "strange" fractal is all speculative and does not exist in reality. We are just exploring the physics of Black Holes, and many of our cherished believes may have to be scraped to the science of reality. Believing in these Fractal Universes is like believing that the world is flat, and we are the center of the universe. If these universes do exist then they are gateways to universes outside our own. Space and time are limitless and the number of universes, outside our own, is limitless. Maybe wormholes exits through these Black Holes, but Fractal Universes don't exist.
Every point of it is the exact center of an infinite Universe. There is no direction left or right of center, up or down from center, center point is every point everywhere whatsoever in such an infinite. Some of what you say is not bad, Not bad at all. But "fractal....does not exist in reality." "....., But Fractal Universes don't exist." There you imploded. Like the rest of us who make claims on cosmology and have to face naysayers, prove it! Prove fractal universes don't exist.
An infinite Universe will include an infinity of [possible] differences, different universes, within the boundarylessness going away from every point. But, eventually, what goes away in the infinity of universes, as to differences, will begin to develop, come to, a difference that is the exact twin of the original point universe. Not exactly the same universe, not at all the same universe, but being an exact twin down to the very last particle, and everything else, of it.
Even being an infinite distance apart, all of an infinity of such twins spread infinitely far apart across an infinity, being exact twins down to the last particle, I long ago began to wonder if there was the possibility of entanglement. If there is the possibility of "spooky action" at an [infinite] distance. That would mean boundaries also entangling with boundaries...and on and on and on. At that point, in that realization of potential entanglement, you are now dealing in a hyper-finite rather than complete infinity. Or, rather, a hyper-finite along with, mixed with, infinity. Laid onto infinity (essentially singularly planed). The infinity still remains, fully remains, yet it also transforms, reduces, even rises, to fractalization (one fractal, mirrored to infinity in self-similarity). Chaos Theory's grain, smooth, grain, smooth.... (finite, infinite, finite, infinite...), vertical layering to infinity (ultimately to end in; is it grainy finite? Is it smooth infinity?).