Fractal trees and Horton's laws |
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| Authors: | Juan M García-Ruiz and 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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| Keywords: | fractal geometry quantitative geomorphology fluvial drainage systems |
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