• 论文 •

### 城市化:相变与自组织临界性

1. 北京大学地理科学研究中心 北京100871
• 收稿日期:2003-11-13 修回日期:2004-02-13 出版日期:2004-06-15 发布日期:2004-06-15
• 作者简介:陈彦光(1965-),河南罗山人,副教授。主要从事地理分形和地理系统的空间复杂性研究。
• 基金资助:

美国UrbanChinaResearchNetworkSmallGrantProgram资助课题;国家自然科学基金重点资助项目(40335051)

### Urbanization as phase transition and self-organized critical process

CHEN Yan guang

1. Department of Geography, Peking University, Beijing 100871,China
• Received:2003-11-13 Revised:2004-02-13 Online:2004-06-15 Published:2004-06-15

Abstract:

This paper discusses the property and marks of urbanization as a self organizing process, which can be thought of as a kind of phase transition from a rural to an urban settlement system. Several empirical observations including fractal structure and rank size distribution can be used to identify the self organized criticality (SOC) of urbanization dynamics. Fractal structure such as central place landscapes in spatial field and the rank size distribution associated with Zipf ’s law in hierarchical field always ‘emerge ’ while urban systems in a region approach to the self organized critical state of urbanism. The central place hierarchy can be characterized with a set of scaling laws as follows: N m=N 1r m-1 n,P m=P 1r 1-m m,A m=A 1r 1-m a . From these exponential scaling laws, we can derive the power laws such as the three parameter Zipf law, P(r)=C(r-ζ) -d , and the law of allometric growth, A m=ηP b m .The exponential distribution indicates random process, while the power law implies some order in complex systems, but we find the unity of opposites between order and chaos of urban systems through the derivation of power laws from the exponential type scaling laws. Moreover, this means that the spatial network of central places and the hierarchical structure of city size distribution reach the same goal by different routes. This in fact corroborates the viewpoint that both the urban hierarchy and spatial network represent the different sides of the same coin. The self organized networks of cities usually become scale free because of the dynamics of urbanization. The map of the urban network patterns in hierarchical field is just the rank size distribution, which appears in the larger picture, not at the level of an individual city. Once the distribution forms, it will become very stable over a long period of time. The formation of the scale free network of cities associated with the rank size distribution is an information rich evolution, which can be simulated using cellular automata (CA) models, cellular space (CS) model, multi agent system (MAS), and so on. Simulation as an experimental tool may be very useful for us to research spatial complication proceeding from urbanization dynamics. However, the simulation based on computer graphics doesn't help us conceptually in understanding the rules of behavior of urban systems at the higher level. As a complement, post modern mathematical theory esp. fractal geometry, chaos mathematics, renormalization group, etc., will play a significant role in the studies of self organizing urbanization.