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Mandelbrot's (1982) hypothesis that river length is fractal has been recently substantiated by Hjelmfelt (1988) using eight rivers in Missouri. The fractal dimension of river length, d , is derived here from the Horton's laws of network composition. This results in a simple function of stream length and stream area ratios, that is, d = max (1, 2 log R L /log R A ). Three case studies are reported showing this estimate to be coherent with measurements of d obtained from map analysis. The scaling properties of the network as a whole are also investigated, showing the fractal dimension of river network, D , to depend upon bifurcation and stream area ratios according to D = min (2, 2 log R B /log R A ). These results provide a linkage between quantitative analysis of drainage network composition and scaling properties of river networks.
Rosso et al. (Fri,) studied this question.