研究城市规模分布的分形特征,修正了一些位序-规模模型,将历史上出现的有关城市规模分布的模型统一在分形形式之下,并给出了具有一般意义的三参数Zipf模型:P(k)=A (K-a)^-q。将Zipf维数与大自然1/f^U起伏的U指数进行类比,认为分维D=1/q=1是一种先验的优化维数,进而提出结构优化的1/r型城市位序-规模分布,以此作为城市体系等级结构规划的依据之一。

Fractals of city-size distribution were studied, and the related mathematical models were compared with one another, revised, and synthesized into the general fractal model on rank-size rule:P(k)=A(K-a)^-q.The fractal dimensions of size distributions of cities were compared with the β-exponent of 1/f^U noise in nature and the 1/r-distribution of city-sizes (Zipf dimension q=1) was presented as the optimumized distribution.It was demonstrated that fractals are essentially orders of hierarchical sturcture of urban systems and D=1/q=1 is the optimum dimension of city-size distributions.