Stochastic self-similar processes and random walk in nature

In this paper we consider the result which was obtained by the first author of the present work to describe scaling rules in nature, R(N) = (h/mnc)N Φ , in connection with the well-know RandomWalk. By adopting this prospect, we present the result as a Brownian motion process developed as a limit of a Random Walk in the context of Mohamed El Naschie’s E(∞) Cantorian space-time applied in cosmology.