中心地体系与水系分形结构的相似性分析——关于人—地对称关系的一个理论探讨  

Studies of Analogies of Fractal Structure between River Networks and Systems of Central places: A Theoretical Approach to the Symmetry between Physical and Human Geographical Systems

作　　者：陈彦光[1] 刘继生[2] 

机构地区：[1]北京大学城市与环境学系,北京100871 [2]东北师范大学地理系,长春130024

出　　处：《地理科学进展》2001年第1期81-88,共8页Progress in Geography

基　　金：国家自然科学基金资助项目 !(40 0 71 0 35)

摘　　要：以城市体系与水系的分形结构相似性为实例 ,探讨人文地理系统与自然地理系统的对称性及其破缺特征。首先建立城市人口—河流长度、城区面积—流域面积、 (某一级别的 )城市数目— (某一等级的 )河流数目等测度对应关系 ;然后证明基于中心地理论的Beckmann城镇等级—规模模型与 Horton水系构成第一、第二定律数理同构 ,关于城市人口—城区面积的异速生长关系模型与关于主河道长度—流域面积的几何测度关系模型以及 Horton水系构成的第二、第三定律数理同构 ;进而提出 :城市体系与水系分形结构的相似性实质上是自然—人文地理系统的对称性 ,只是这种对称关系存在一定程度的破缺 。It is demonstrated in the paper that the cascade structure of river networks is analogous to that of urban systems or systems of central places, i.e.,the two kind of systems have the same fractal recurrence. Where mathematical models are concerned, the first and second ones of Horton's laws of drainage composition is same to Beckmann's models of city hierarchies which are based on central place theory; Hack's law, which can be derived from the second and third Horton's models, is same to allometric relationships between area and population of urban systems, the latter is connected with Beckmann's models and thereby with central place theory. A conclusion can be drawed as follows: urban systems as well as central places are symmetrical with river networks, as is generalized, we have a conclusion that human geographical systems are symmetrical with physical geographical systems, with the symmetry breaking to some extent in some aspects.

关 键 词：中心地 水系 人地关系 分形 城市体系 人文地理系统 自然地理系统 

分 类 号：K901[历史地理—人文地理学] P90[天文地球—自然地理学]