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A scaling approach to evaluating the distance exponent of the urban gravity model

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  • Chen, Yanguang
  • Huang, Linshan

Abstract

The gravity model is one of important models of social physics and human geography, but several basic theoretical and methodological problems remain to be solved. In particular, it is hard to explain and evaluate the distance exponent using the ideas from Euclidean geometry. This paper is devoted to exploring the distance-decay parameter of the urban gravity model. Based on the concepts from fractal geometry, several fractal parameter relations can be derived from the scaling laws of self-similar hierarchies of cities. Results show that the distance exponent is just a scaling exponent, which equals the average fractal dimension of the size measurements of the cities within a geographical region. The scaling exponent can be evaluated with the product of Zipf's exponent of size distributions and the fractal dimension of spatial distributions of geographical elements such as cities and towns. The new equations are applied to China's cities, and the empirical results accord with the theoretical expectations. The findings lend further support to the suggestion that the geographical gravity model is a fractal model, and its distance exponent is associated with a fractal dimension and Zipf's exponent. This work will help geographers understand the gravity model using fractal theory and estimate the distance exponent using fractal modeling.

Suggested Citation

  • Chen, Yanguang & Huang, Linshan, 2018. "A scaling approach to evaluating the distance exponent of the urban gravity model," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 303-313.
    • Handle: RePEc:eee:chsofr:v:109:y:2018:i:c:p:303-313
    DOI: 10.1016/j.chaos.2018.02.037
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    1. Kang, Chaogui & Ma, Xiujun & Tong, Daoqin & Liu, Yu, 2012. "Intra-urban human mobility patterns: An urban morphology perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1702-1717.
    2. R White & G Engelen, 1993. "Cellular Automata and Fractal Urban Form: A Cellular Modelling Approach to the Evolution of Urban Land-Use Patterns," Environment and Planning A, , vol. 25(8), pages 1175-1199, August.
    3. repec:cai:popine:popu_p1998_10n1_0240 is not listed on IDEAS
    4. Chen, Yanguang, 2011. "Fractal systems of central places based on intermittency of space-filling," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 619-632.
    5. Chen, Yanguang, 2015. "The distance-decay function of geographical gravity model: Power law or exponential law?," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 174-189.
    6. Chen, Yanguang, 2014. "Multifractals of central place systems: Models, dimension spectrums, and empirical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 266-282.
    7. Chen, Yanguang, 2016. "The evolution of Zipf’s law indicative of city development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 555-567.
    8. Cerqueti, Roy & Ausloos, Marcel, 2015. "Evidence of economic regularities and disparities of Italian regions from aggregated tax income size data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 187-207.
    9. Lucien Benguigui & Daniel Czamanski & Maria Marinov & Yuval Portugali, 2000. "When and Where is a City Fractal?," Environment and Planning B, , vol. 27(4), pages 507-519, August.
    10. Yanguang Chen, 2012. "Zipf's Law, Hierarchical Structure, and Cards-Shuffling Model for Urban Development," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-21, April.
    11. Filippo Simini & Marta C. González & Amos Maritan & Albert-László Barabási, 2012. "A universal model for mobility and migration patterns," Nature, Nature, vol. 484(7392), pages 96-100, April.
    12. Yu Liu & Zhengwei Sui & Chaogui Kang & Yong Gao, 2014. "Uncovering Patterns of Inter-Urban Trip and Spatial Interaction from Social Media Check-In Data," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-11, January.
    13. Chen, Yanguang & Zhou, Yixing, 2008. "Scaling laws and indications of self-organized criticality in urban systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 85-98.
    14. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    15. Chen, Yanguang, 2012. "The mathematical relationship between Zipf’s law and the hierarchical scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3285-3299.
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    Cited by:

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    2. Fernández-Rosales, Iván Yair & Angulo-Brown, Fernando & Pérez-Campuzano, Enrique & Guzmán-Vargas, Lev, 2020. "Distance distributions of human settlements," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Rong Guo & Tong Wu & Mengran Liu & Mengshi Huang & Luigi Stendardo & Yutong Zhang, 2019. "The Construction and Optimization of Ecological Security Pattern in the Harbin-Changchun Urban Agglomeration, China," IJERPH, MDPI, vol. 16(7), pages 1-18, April.

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