A new formula is derived for the information dimension D1 of the unscreened surface of a fractal pattern (its fractal dimension df). The formula yields D1=d-1, independent of df, when Brownian particles are used to probe the surface. The extension is made to the case of the probability distribution due to the growth rule of the model. The approximate expression of the generalized dimension Dq (q1) is then derived. All the results are found to be in very good agreement with our numerical results and the available data reported so far.
ASJC Scopus subject areas
- Physics and Astronomy(all)