  Beginning with the most general fractal strings/sprays construction recently
expounded in the book by Lapidus and Frankenhuysen, it is shown how the
complexified extension of El Naschie's Cantorian-Fractal spacetime model
belongs to a very special class of families of fractal strings/sprays whose
scaling ratios are given by suitable pinary (pinary, $p$ prime) powers of the
Golden Mean. We then proceed to show why the logarithmic periodicity laws in
Nature are direct physical consequences of the complex dimensions associated
with these fractal strings/sprays. We proceed with a discussion on
quasi-crystals with p-adic internal symmetries, von Neumann's Continuous
Geometry, the role of wild topology in fractal strings/sprays, the
Banach-Tarski paradox, tesselations of the hyperbolic plane, quark confinement
and the Mersenne-prime hierarchy of bit-string physics in determining the
fundamental physical constants in Nature.
