[micheles]

The article is badly written. This has nothing to do with fractals, they are talking about the assumption that there is an UV fixed point for all physical laws, which can even be true and personally like. It means there are no ultraviolet divergences and that at some point quantum field theory becomes finite. Over a certain large mass scale (which still can be much smaller than the Plank scale) all the coupling constants freeze, there are no radiative corrections and all is simple and well behaved. The problem is, you need some extra fields to do that, with some symmetry cancelling the divergences over the mass scale (it does not have to be supersymmetry) and we lack a theory for that. Moreover, the low energy physics will be nearly independent from the high energy modifications, so the predictive power is low. Yes, they predicted the Higgs mass, but it could very well be a coincidence. If they could predict something really new, though, then it would become quite interesting.