Fractal geometry of individual river channels and its computer simulation

A new method for analyzing the self‐similarity and self‐affinity of single‐thread channels is proposed. It permits the determination of the fractal scaling exponents, of the characteristic scales, and the evaluation of the degree of anisotropy for self‐similar fractal lines. Based upon the application of this method to the Dniester and Pruth rivers we established the self‐similarity of the river pattern on small scales and the self‐affinity on large scales. For these rivers we obtained the fractal scaling exponents, the characteristic scales, and the anisotropy parameters. A computer model has been developed which simulates river patterns whose fractal properties are close to the properties of natural objects. A generalized model of fractal behavior of natural rivers is proposed. On the basis of self‐affinity of natural and simulated rivers on large scales, a hypothesis has been formulated which explains the violation of the dimension principle in the well‐known relation between the river length and the catchment area.