Unified view of scaling laws for river networks.

Fractal river networks, Horton's laws and Tokunaga cyclicity

The structure and scaling of river networks characterized using fractal dimensions related to Horton's laws is assessed. The Hortonian sealing 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 eyclicity presents an alterna...

Fractals and fractal dimension of systems of blood vessels: An analogy between artery trees, river networks, and urban hierarchies

An analogy between the fractal nature of networks of arteries and that of systems of rivers has been drawn in the previous works. However, the deep structure of the hierarchy of blood vessels has not yet been revealed. This paper is devoted to researching the fractals, allometric scaling, and hierarchy of blood vessels. By analogy with Horton-Strahler’s laws of river composition, three exponent...

Geometry of river networks. I. Scaling, fluctuations, and deviations.

This paper is the first in a series of three papers investigating the detailed geometry of river networks. Branching networks are a universal structure employed in the distribution and collection of material. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description o...

Influence of terrain on scaling laws for river networks

Harmonic scaling laws and underlying structures

Based on the effective field theory philosophy, a universal form of the scaling laws could be easily derived with the scaling anomalies naturally clarified as the decoupling effects of underlying physics. In the novel framework, the conventional renormalization group equations and Callan-Symanzik equations could be reproduced as special cases and a number of important and difficult issues aroun...