Horton定律及分枝网络结构的分形描述

Horton Law and Fractal Nature of Branching Networks

摘要: 在Horton定律的基础上提出分枝网络结构的端头构成的集合的分形维数更具有实际意义,并得出了端头集合的自相似维数。在此基础上,又给出了具有两个不同分枝长度比的两分枝结构的端头的多分形描述,并定性地分析了其f(α)～α谱和Dq～q谱。讨论了其在实际河流网络中的意义。

Abstract: Based on Horton law,this paper proposes the property of tip set of branching networks which is more significant in actual works,and the self-similar dimension of tip set is obtained.Then multifractal nature of tip set of branching networks with two different branching lenghth ratios is described,and its f(α)～α spectrum as well as D_q～q spectrum are analysised qualitatively.Finally,their significance in the real river networks are discussed.