The fractal nature of river networks

Abstract

Ever since Mandelbrot (1975, 1983) coined the term, there has been speculation that river networks are fractals. Here we report analyses done on river networks to determine their fractal structure. We find that the network as a whole, although composed of nearly linear members, is practically space filling with fractal dimension near 2. The empirical results are backed by a theoretical analysis based on long‐standing hydrologic concepts describing the geometric similarity of river networks. These results advance our understanding of the geometry and composition of river networks.