城市形态边界维数与常用空间测度的关系  

Fractal measurement of urban boundaries and compactness or circularity ratios of cities

作　　者：陈彦光[1] 刘继生[2] 

机构地区：[1]北京大学地理科学研究中心,北京100871 [2]东北师范大学中国东北研究院,吉林长春130024

出　　处：《东北师大学报（自然科学版）》2006年第2期126-131,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(40371039)

摘　　要：在城市地理系统对称发育的假设条件下,从标准圆出发,基于城市形态的几何测度关系推导出边界维数的倒数与紧凑度以及圆形率的半对数关系.借助国内有关学者发表的观测数据验证了推导结果.指出,城市形态的边界维数是一个宏观概念,而紧凑度和圆形率则是一种微观概念.边界维数与紧凑度的数理关系反映城市地理系统宏观规律与微观结构的内在联系,这类关系正是地理空间复杂性关注的问题之一.Fractal dimension of urban form is a notion defined at macro level, while compactness ratio or circularity ratio is a spatial measurement of cities defined at micro level. The connection between the fractal dimension and compactness or circularity ratio can link macro state associated with simplicity and micro state associated with complexity from one angle of view. In this paper,an exponential relation between the reciprocal of fractal dimension of urban boundaries and compactness ratio or circularity ratio is derived from the assumption based on standard roundness. The equations are given as follows, Co = αexp （b/D）, Ci = βexp（2b/D）, where Co denotes compactness ratio, Ci represents circularity ratio, D is the fracta/dimension of boundaries,and α,β and b are parameters. 31 large cities of China are taken as examples to validate the two mathematical expressions and its inference, and the results are satisfying. The relations between macro - and micro- levels will redound to our understanding the spatial order emerging between simplicity and complexity.

关 键 词：城市形态 分形 边界维数 紧凑度 圆形率 空间复杂性 

分 类 号：K928.5[历史地理—人文地理学]