Let's get physical!
So you want to apply this in Physics? This has already happened. Laurent Nottale has tried a fractal approach to spacetime. He gets the expected Higgs mass wrong though and predicts that the large-scale structure of the universe should be self-similar, of which there is not a whole lot of evidence (it's more like a synaptic mess, innit). Maybe he tries too hard:
http://luth2.obspm.fr/~luthier/nottale/ukrechel.htm