城市化:相变与自组织临界性

Urbanization as phase transition and self-organized critical process

城市化的本质是一种自组织临界相变过程 ,在时间和空间上分别联系着自组织临界性(SOC)和空间复杂性。城市化过程作为SOC有 3个方面的标志 :时间方向的 1/ f涨落、空间方面的分形结构和等级方式的Zipf定律 ,其共性是无标度性。分形中心地景观和位序 -规模分布分别是城市化自组织临界过程在空间和等级两个领域的实证判据。在城市化的临界相变过程中 ,城市体系通常演化为无标度网络 ,而位序 -规模法则乃是空间领域的无标度性在等级领域的结构性“投影”。基于SOC思想研究城市化过程有助于理解自组织城市网络的复杂空间动力学 。

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.