Fractal trees and Horton's laws |
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Authors: | Juan M García-Ruiz Fermín Otálora |
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Institution: | 1. Instituto Andaluz de Geología Mediterránea, C.S.I.C.-Universidad de Granada, Avda. Fuentenueva s/n, 18002, Granada, Spain
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Abstract: | 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. |
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