Fractal River Networks, Hortons laws and Tokunaga cyclicity

David G. Tarboton, Utah State University


The structure and scaling of river networks characterized using fractal dimensions related to Horton's laws is assessed. The Hortonian scaling framework is shown to be limited in that strict self similarity is only possible for structurally Hortonian networks. Dimension estimates using the Hortonian scaling system are biased and do not admit space filling. Tokunaga cyclicity presents an alternative way to characterize network scaling that does not suffer from these problems. Fractal dimensions are presented in terms of Tokunaga cyclicity parameters.