WATER EROSION AS A FRACTAL GROWTH-PROCESS

The time evolution of river patterns and earth's relief is simulated o n lattice by modeling the process of water erosion. Starting from a ra ndomly perturbed surface, the river pattern and earth's relief develop simultaneously. The river pattern becomes stationary after all lakes have vanished. In the stationary state the river pattern shows some fr actal properties such as a power-law size distribution of the drainage basin area and Horton's laws. The fractalities are shown to be not ex actly self-similar but self-affine. A mean-field theory for the river pattern is discussed.