The aim of this work is the analysis of multifractals in the context of Mohamed El Naschie’s ϵ ( ∞ ) Cantorian space–time applied to cosmology. As starting point we consider the results of the first author of the present paper describing scaling rules in nature, R ( N ) = ( h / m n c ) N ϕ . Then, we use multifractal analysis to show that the result, already developed by the authors as Brownian motion, is a Multifractal process. Indeed, Brownian paths play a crucial role if considered to be a multifractal. Moreover, we summarize some recent results concerning fractal structure and the Brownian paths in order to calculate fractal dimension and characteristic parameters for large scale structures and for the atomic elements that live in an El Naschie’s ϵ ( ∞ ) Cantorian space–time.