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The Geometric Origins of Complex Cities

  • Ruiqi Li
  • Lei Dong
  • Xinran Wang
  • Jiang ZhangEmail author
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

Due to the rapid urbanization, cities have become a hot topic. Extensive complex phenomena, such as scaling laws with respect to population, morphology, spatial distribution within cities have been revealed and validated by the empirical studies. Yet there’s still no clear answer to the question that what’s the underlying mechanism responsible for these observed complex phenomena. Most of previous studies only focus on one aspect of the city. However, focusing on only one aspect may lose the whole picture of it. Based on a very simple “matching growth” rule and two more simple assumptions, which are all performed locally, we propose a simple model which can derive most of observed macro scaling relations and spatial distribution. All these theoretical deductions can be well supported by empirical data. And the consistency between the exponents of different cumulative spatial distribution may indicates that the city really follows the rules we assumed.

Keywords

Fractal Dimension Road Network City Center Voronoi Diagram Allometric Scaling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

J. Zhang thanks for the discussions with Prof. Bettencourt in Santa Fe Institute, doctor Wu in Arizona University and Prof. Wang and Chen in Beijing normal university, acknowledges the support from the National Natural Science Foundation of China under Grant No. 61004107 and No. 61174165.

References

  1. 1.
    Montgomery, M.R.: The urban transformation of the developing world. Science 319, 761–764 (2008)ADSCrossRefGoogle Scholar
  2. 2.
    Bettencourt, L.M., Lobo, J., Helbing, D., Kühnert, C., West, G.B.: Growth, innovation, scaling, and the pace of life in cities. Proc. Natl. Acad. Sci. 104, 7301–7306 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    Bettencourt, L.M., Lobo, J., Strumsky, D.: Invention in the city: increasing returns to patenting as a scaling function of metropolitan size. Res. Policy 36, 107–120 (2007)CrossRefGoogle Scholar
  4. 4.
    Bettencourt, L., West, G.: A unified theory of urban living. Nature 467, 912–913 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    Bettencourt, L.M., Lobo, J., Strumsky, D., West, G.B.: Urban scaling and its deviations: revealing the structure of wealth, innovation and crime across cities. PloS ONE 5, e13541 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    Glaeser, E.: Cities, agglomeration, and spatial equilibrium. Oxford University Press (2008)Google Scholar
  7. 7.
    Mumford, L.: The City in history. Its origins, its transformation, and its prospects. Harcourt, Brace & world (1961)Google Scholar
  8. 8.
    Geddes, P.: Cities in evolution: an introduction to the town planning movement and to the study of civics. Williams & Norgate, London (1915)Google Scholar
  9. 9.
    Kostof, S.: The city shaped urban patterns and meaning throughout history. Bulfinch, Boston (1991)Google Scholar
  10. 10.
    Batty, M.: The size, scale, and shape of cities. Science 319, 769–771 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    Zipf, G. K.: Human behavior and the principle of least effort. Addison-Wesley Press (1949)Google Scholar
  12. 12.
    Zanette, D. H.: Zipf’s law and city sizes: a short tutorial review on multiplicative processes in urban growth. arXiv preprint arXiv:0704.3170 (2007)
  13. 13.
    Eeckhout, J.: Gibrat’s law for (all) cities. American Economic Review, pp. 1429–1451 (2004)Google Scholar
  14. 14.
    Gabaix, X.: Zipf’s law for cities: an explanation. Quarterly Journal of Economics, pp. 739–767 (1999)Google Scholar
  15. 15.
    Nordbeck, S.: Urban allometric growth. Geogr. Ann. Ser. B Human Geogr. 53, 54–67 (1971)CrossRefGoogle Scholar
  16. 16.
    Rozenfeld, H.D., Rybski, D., Gabaix, X., Makse, H.A.: The area and population of cities: new insights from a different perspective on cities. Am. Econ. Rev. 101, 2205–2225 (2011)CrossRefGoogle Scholar
  17. 17.
    Batty, M., Ferguson, P.: Defining city size. Environ. Planning B Planning Des. 38, 753–756 (2011)CrossRefGoogle Scholar
  18. 18.
    Batty, M., Longley, P.A.: Fractal cities: a geometry of form and function. Academic Press (1994)Google Scholar
  19. 19.
    Makse, H.A., Havlin, S., Stanley, H.: Modelling urban growth. Nature 377, 19 (1995)CrossRefGoogle Scholar
  20. 20.
    Pan, W., Ghoshal, G., Krumme, C., Cebrian, M., Pentland, A.: Urban characteristics attributable to density-driven tie formation. Nat. Commun. 4 (2013)Google Scholar
  21. 21.
    Bettencourt, L.M.: The origins of scaling in cities. Science 340, 1438–1441 (2013)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Doxiadis, C.A.: Ekistics, the science of human settlements. Science 170, 393–404 (1970)ADSCrossRefGoogle Scholar
  23. 23.
    Smeed, R.J.: The traffic problem in towns. Manchester Statistical Society (1961)Google Scholar
  24. 24.
    Batty, M., Kim, K.S.: Form follows function: reformulating urban population density functions. Urban Stud. 29, 1043–1069 (1992)CrossRefGoogle Scholar
  25. 25.
    Clark, C. Urban population densities. J. R. Stat. Soc. A (General) 114, 490–496 (1951)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Systems ScienceBeijing Normal UniversityBeijingChina
  2. 2.School of ArchitectureTsinghua UniversityBeijingChina
  3. 3.College of Resources Science and TechnologyBeijing Normal UniversityBeijingChina

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