中心地体系中蕴含着分形结构,具有多分维特征。本文借助koch雪花和随机Sierpinski图形揭示了中心地k=3体系和k=4体系的生成机制,提出了城乡聚落体系和城市-交通网络的两种分形模型,这些模型的分维与S.Arlinghaus的发现具有对应性。

In the paper,an approach was made to the fractals and fractal dimensions in systems of central places.Two fractal models of systems of cities and towns were studied; one is Koch snowflake model (KSM),which corresponds to the central place pattern of k=3,and can be used to imitate urban systems;the other is Sierpinski triangular network modol(STN),which,presented for the first time,corresponds to the central place pattern of k=4,and can be used to simulate transport network based on urban agglomerations.The fractal dimensions of the former are calculated as 1.631 and 1.771,and, the latter,is 1.585,which correspond with the results given by S.L.& W.C.Arlinghaus. Fractal dimensions of some examples were tabulated to demonstrate the fractal central place theory.