Self-Affinity of Scheidegger′s River Patterns

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  • Self-Affinity of Scheidegger’s River Patterns
  • Self Affinity of Scheidegger s River Pa

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We investigated the scaling property of the drainage basin patterns generated by computer-simulation of the Scheidegger’s river network model, which is a type of directed percolation model. Growth exponents are obtained from the inclination of the log-log plot of the length L (parallel direction) and the width W (perpendicular direction) of the drainage basins as a function of the drainage area A, i.e., L∼Aν⁄⁄ and W∼Aν⊥. The values are found to be ν⁄⁄=2⁄3 and ν⊥=1⁄3, and the patterns are not self-similar, but self-affine. The relation ν⁄⁄+ν⊥=1 indicates that the inner structure is nonfractal or compact. Theoretical considerations are also given to these results.

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