Fractal trees and Horton''s laws

Fractal trees as a model for drainage systems are described in its generalized non-homogeneous form from the viewpoint of fractal geometry. Box covering techniques are used to show the numerical equivalence between the Hausdorff-Besicovitch dimension and the similarity dimension of the fractally-dominant dust formed by the sources. In this way, the similarity relationD=log (N)/log (1/r) is reinterpreted in terms of bifurcation and length ratio (r_B andr_L) asD=log (r_B)/log (r_L). We test this relation for non-homogeneous exact fractal trees and two natural drainage systems. The fact thatr_B andr_L are common parameters in quantitative geomorphology allows a trivial stimation of the fractal dimension of well-known drainage basins.