Minimum energy dissipation river networks with fractal boundaries.

The effects of the entire drainage area boundary on the drainage basins and their size distributions have been studied using the minimum energy dissipation model for river networks. A simple scaling relationship \ensuremath{\tau}=1+D/2 between the values of the exponents \ensuremath{\tau} in the power law basin size distibutions and the fractal dimension D of the boundary of the entire drainage area has been established. The scaling relationship has been tested using simulations, with external perimeters (D=4/3) or hulls (D=7/4) of invasion percolation clusters, as the boundaries for the entire drainage areas.