Estimated Generalized Dimensions of the River Networks

This work concerns a numerical estimation of the generalised fractal dimension of six river networks in Southern Italy, extracted from digitised maps on a 1:25,000 scale. The estimation is carried out through the method introduced by Pawelzik and Schuster, based on an extension of the correlation integral by Grassberger and Procaccia. We analysed the spectra of the generalised dimensions Dq and the multi-fractal spectra f(a). The results are in agreement with the ones previously obtained through the use of standard box-counting techniques: they indicate that the investigated river networks are multi-fractal structures, with support dimensions ranging between 1.7 and 1.9, and appear not to be plane-filling sets. In the case of the Corace river, the multi-fractal spectrum of the whole river network approaches the envelope of the spectra of substructures corresponding to different hortonian stream orders.