Ha ha, hi O'Tink yes I kinda gave your Q my all, here...but I am guessing my answer will prove out to be accurate, someday in the future...
You prolly already aware, that is the magic of the fractal equations; you just keep plugging the result back in to the equation, and there is no limit, there is no bottom as to how deep you can go. And then trees, blood vessels, ferns, a shoreline, the human nervous system, on and on, all constructed fractally! (Is that a word?)
Well like you Stephen Hawking says NO! Unlike fractals, matter is prolly not infinitely deep (but he admits no one knows for sure); he implies that, as you go down finer and finer, Planck's constant will turn out to be the lower limit, the essential "grittiness" of the universe, of creation, so to speak; it all ends there.
However I think the Hon. Dr. Hawking is wrong in that! (sniff)
Also, I think our consciousness evolves; you and many others here have a very fine consciousness, so just hold on for a wild & beautiful ride into the future, I suspect! (The implication is that if there is a limit, then yes we can [hypothetically at least] construct that brain wiring, if no limit then we can't, and we got to wait for our consciousness to evolve.)
So I have placed a hypothetical bet with Dr. Stephen, and ima collect on it maybe 200 years from now! (Or a thousand years...)