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

  • 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 date: 2009-07-01

  Revised date: 2010-05-16

  Online 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


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.

Cite this article

LAI Shih-Kung, HAN Haoying, YU Ju-Ling, KO Po-Chien . The Formation of Urban Settlement Systems:Computer Experiments and Mathematical Proofs of the Increasing Returns Approach to Power Law[J]. Acta Geographica Sinica, 2010 , 65(8) : 961 -972 . DOI: 10.11821/xb201008007


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