The Formation of Urban Settlement Systems:Computer Experiments and Mathematical Proofs of the Increasing Returns Approach to Power Law
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.
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
[1] Batty M. Rank clock. Nature, 2006, 444: 592-596.
[2] Zipf G K. Human Behavior and the Principle of Least Effort. New York: Addison-Wesley Press, 1949.
[3] Gibaix X. Zipf's Law for cities: An explanation. Quarterly Journal of Economics, 1999, 14(3): 739-767.
[4] Chen Hsin-Ping. Zipf's Law and the spatial interaction models//Proceedings of Annual Meeting for Regional Science Association, A1-III-1-30, Taipei, 2000.
[5] Bak P, Chen K. Self-organization criticality phenomenon. Journal of Geophysical Studies, 1989, 94: 15635-15637.
[6] Bak P. Self-organizing criticality. Scientific American, 1991, (1): 26-33.
[7] Simon H A. On a class of Skew Distribution Function. Biometrika, 1955, 52: 425-440.
[8] Krugman P. The Self-organizing Economy. Cambridge, Massachusetts: Blackwell Publishers Inc., 1996.
[9] Arthur W B. Increasing Returns and Path Dependence in the Economy. Ann Arbor, Michigan: The University of Michigan Press, 1990.
[10] Arthur W B. Silicon Valley's vocational clusters: When do increasing returns imply monopoly? Mathematical Social Sciences, 1990, (19): 235-251.
[11] 王振玉. 都市及区域发展统计汇编. 台北: 行政院经济建设委员会都市及住宅发展处, 2003.
[Wang Zhen-Yu. Collections of Statistical Data for Urban and Regional Development, Taipei: City and Housing Development Division,. Economic Construction Commission, The Executive Council, 2003.]
[12] 邵波, 潘强. 浙江省城乡建设用地规模和优化布局研究. 杭州: 浙江大学出版社, 2006.
[Shao Bo, Pan Qiang. Urban and Rural Construction Land Area and the Improvement of Its Spatial Distribution in Zhejiang Province. Hangzhou:Zhejiang University Press, 2006.]
[13] Arthur W B, Ermoliev Y M, Kaniovski Y M. Path-dependent processes and the emergence of macro-structure. European Journal of Operational Research, 1987, 30: 294-303.
/
〈 | 〉 |