地理学报

地理学报 ›› 2010, Vol. 65 ›› Issue (8): 961-972.doi: 10.11821/xb201008007

• 城市地理 • 上一篇    下一篇

都市聚落系统的形成规律——递增报酬与幂次法则的计算机与数理仿真

赖世刚1,2, 韩昊英1, 于如陵3, 柯博晟4   

  1. 1. 浙江大学土地科学与不动产研究所,杭州310029;
    2. 台北大学不动产与城乡环境学系,台北;
    3. 昆山科技大学不动产经营系,台南;
    4. 台北大学都市计划研究所,台北
  • 收稿日期:2009-07-01 修回日期:2010-05-16 出版日期:2010-08-20 发布日期:2010-08-20
  • 通讯作者: 韩昊英, 男, 副教授, 主要从事城市规划、土地利用规划与控制等研究, E-mail: hanhaoying@zju.edu.cn
  • 作者简介:赖世刚, 男, 教授, 主要从事都市、复杂与规划研究, E-mail: lai@mail.ntpu.edu.tw
  • 基金资助:

    国家自然科学基金项目(50908200); 教育部留学回国人员启动基金项目(J20091217)

The Formation of Urban Settlement Systems:Computer Experiments and Mathematical Proofs of the Increasing Returns Approach to Power Law

LAI Shih-Kung1,2, HAN Haoying1, YU Ju-Ling3, KO Po-Chien4   

  1. 1. Institution of Land Science and Property Management, Zhejiang University, Hangzhou 310029, China;
    2. Department of Real Estate and Built Environment, National Taipei University, Taipei, China;
    3. Department of Real Estate Management, Kun Shan University of Technology, Tainan, China;
    4. Graduate Institute of Urban Planning, National Taipei University, Taipei, China
  • Received:2009-07-01 Revised:2010-05-16 Online:2010-08-20 Published:2010-08-20
  • Supported by:

    National Natural Science Foundation of China, No.50908200; No.E080201; The Scientific Research Foundation of the Ministry of Education for Returned Chinese Scholars, No.J20091217

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摘要：

幂次法则是一个普遍存在于自然科学与社会科学界的现象,在都市体系中亦可观察到此一现象。过去的文献仅仅对于幂次法则现象进行了观察和解释,并未能完整地解释其形成的机制。本研究尝试由复杂理论中“递增报酬”的观念来探讨幂次现象的成因,采用计算机程序来仿真都市聚落体系形成的过程,并观察递增报酬与幂次现象之关系。该仿真包含了3 种不同的区位发展吸引模式,分别为相邻关系、规模吸引以及同时考虑规模与相邻的混合模式。计算机仿真显示：① 规模吸引与混合两种模式比相邻吸引模式能够更好地解释都市聚落的成长;② 依照递增报酬法则而仿真形成的都市聚落,与幂次现象呈高度相关。随后的数理仿真演算显示,幂次法则为一统计上的普遍现象,但在递增报酬等经济因素驱动下的都市聚落体系结构与真实的状况较为吻合。因此我们推测,递增报酬极可能是形成真实世界幂次现象的机制之一。

关键词: 计算机仿真, 幂次现象, 递增报酬, 都市聚落体系

Abstract:

The power law is a phenomenon that can be widely observed in both natural and social environments, and is evident in the urban settlement systems. Previous studies successfully observed and identified the power law phenomenon, but have not given a complete explanation about how the power law forms. Viewing cities as complex systems, this research attempts to explore why power law emerges from the increasing-returns to urban scale in the complexity theory by designing and implementing computer experiments based on the Microsoft Visual Basic software to simulate the growth of urban settlements and observing the relationship between increasing returns and power law. Three basic patterns of urban growth are simulated in this research: neighborhood attraction, scale attraction, and mixed attraction. The results of the computer experiments suggest that (1) the scale-attraction and mixed-attraction patterns explain better the growth of urban settlements than the neighborhood-attraction pattern; and (2) a close relationship exists between the emergent power law phenomenon and the urban systems that are formed through the three simulation patterns under the increasing returns assumption. In addition, the mathematical simulation implies that power law is a universal phenomenon in statistics, and the formation of urban settlement systems is driven by economic factors, such as increasing returns. Therefore, we argue that increasing returns would be one of the underlying mechanisms through which the power law phenomenon emerges in the real world.

Key words: computer experiment, power law, increasing returns, urban settlement systems