Analogies between urban hierarchies and river networks: Fractals, symmetry, and self-organized criticality

作者：Chen Yanguang^*

来源：Chaos Solitons & Fractals, 2009, 40(4): 1766-1778.

DOI：10.1016/j.chaos.2007.09.059

A pair of nonlinear programming models is built to explain the fractal structure of systems of cities and those of rivers. The hierarchies of cities can be characterized by a set of exponential functions, which is identical in form to the Horton-Strahler's laws of the river networks. Four power laws can be derived front these exponential functions. The evolution of both systems of cities and rivers are then represented as nonlinear dual programming models: to maximize information entropy subject to a certain energy use or to minimize energy dissipation subject to certain information capacity. The optimal solutions of the programming problems are just the exponential equations associated with scaling relations. By doing so, fractals and the self-organized criticality marked by the power laws are interpreted using the idea from the entropy-maximization principle, which gives further weight to the suggestion that optimality of the system as a whole defines the dynamical origin of fractal forms in both nature and society.

• 出版日期2009-5-30
• 单位北京大学