城市结构和形态的分形模型与分维测算

A Fractal Study of a City System:Mathematic Models and the Determination of Fractal Dimension

从一般城市动力系统出发，导出具有分形性质的城市异速生长方程、Ｃｏｂｂ－Ｄｏｕｇｌａｓ函数以及城市人口的密度衰减模型等，然后借助密度相关函数引出城市空间结构与形态分维测算的三种基本方法：回转半径法、波谱指数法和关联函数法。

A study was made with fractal geometry in the paper on urban structure and morphology ,aiming at laying a foundation for the theoretical system of fractal urban geography.From equations of a general urban dynamic system,allonetric growth models,Cobb-Douglas function ,and urban population density attenuation formula,etc,were deduced,and then,based on lattice models,three methods of determination of the fractal dimensions of a city system were formulated ,including gyration radius method,spectrum exponent method,and correlation function method,all of which will contribute to systematizing most of the various models of fractal cities advanced formerly.