IDEAS home Printed from https://ideas.repec.org/a/sae/envirb/v33y2006i3p345-364.html
   My bibliography  Save this article

Reinterpreting Central Place Networks Using Ideas from Fractals and Self-Organized Criticality

Author

Listed:
  • Yanguang Chen
  • Yixing Zhou

Abstract

The basic rules of central place networks are abstracted and formulated as three geometric series scaling laws, which can be transformed into several power laws associated with fractal structure. The scaling laws might be the Rosetta Stone to understand the complexity of human geographical systems because they take the form of Horton and Strahler's laws in geomorphology and Gutenberg and Richter's laws in seismology indicative of fractals and self-organized criticality (SOC). An empirical analysis is conducted with the use of data from southern Germany, given by Christaller. The fractal dimensions, D f , of four systems are calculated as follows: D f is 1.733 for Munich, 1.685 for Nuremberg, 1.837 for Stuttgart, and 1.481 for Frankfurt. SOC theory is employed to interpret the fractality of central places, and the power laws are seen as signatures of feasible optimality, thus yielding further support to the suggestion that optimality of the system as a whole explains the dynamic origin of fractal forms in nature.

Suggested Citation

  • Yanguang Chen & Yixing Zhou, 2006. "Reinterpreting Central Place Networks Using Ideas from Fractals and Self-Organized Criticality," Environment and Planning B, , vol. 33(3), pages 345-364, June.
    • Handle: RePEc:sae:envirb:v:33:y:2006:i:3:p:345-364
    DOI: 10.1068/b31131
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1068/b31131
    Download Restriction: no
    File URL: https://libkey.io/10.1068/b31131?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Claes Andersson & Steen Rasmussen & Roger White, 2002. "Urban Settlement Transitions," Environment and Planning B, , vol. 29(6), pages 841-865, December.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Yanguang, 2009. "Analogies between urban hierarchies and river networks: Fractals, symmetry, and self-organized criticality," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1766-1778.
    2. 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.
    3. Bo Liu & Desheng Xue & Yiming Tan, 2019. "Deciphering the Manufacturing Production Space in Global City-Regions of Developing Countries—a Case of Pearl River Delta, China," Sustainability, MDPI, vol. 11(23), pages 1-26, December.
    4. Zhijun SONG & Linjun YU, 2019. "Multifractal features of spatial variation in construction land in Beijing (1985–2015)," Palgrave Communications, Palgrave Macmillan, vol. 5(1), pages 1-15, December.
    5. Boeing, Geoff, 2017. "Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction," SocArXiv c7p43, Center for Open Science.
    6. François Sémécurbe & Cécile Tannier & Stéphane G. Roux, 2019. "Applying two fractal methods to characterise the local and global deviations from scale invariance of built patterns throughout mainland France," Journal of Geographical Systems, Springer, vol. 21(2), pages 271-293, June.
    7. Qindong Fan & Fengtian Du & Hu Li, 2020. "A Study of the Spatial Form of Maling Village, Henan, China," Sustainability, MDPI, vol. 12(18), pages 1-24, September.
    8. Yanguang Chen & Yixing Zhou, 2003. "The Rank-Size Rule and Fractal Hierarchies of Cities: Mathematical Models and Empirical Analyses," Environment and Planning B, , vol. 30(6), pages 799-818, December.
    9. Yanguang Chen & Jiejing Wang, 2013. "Multifractal Characterization of Urban Form and Growth: The Case of Beijing," Environment and Planning B, , vol. 40(5), pages 884-904, October.
    10. Jian Feng & Yanguang Chen, 2021. "Modeling Urban Growth and Socio-Spatial Dynamics of Hangzhou, China: 1964–2010," Sustainability, MDPI, vol. 13(2), pages 1-25, January.
    11. Yuqing Long & Yanguang Chen & Yajing Li, 2023. "Multifractal scaling analyses of the spatial diffusion pattern of COVID-19 pandemic in Chinese mainland," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-13, December.
    12. Bo Liu & Desheng Xue & Sijun Zheng, 2023. "Evolution and Influencing Factors of Manufacturing Production Space in the Pearl River Delta—Based on the Perspective of Global City-Region," Land, MDPI, vol. 12(2), pages 1-22, February.
    13. Lucien Benguigui & Efrat Blumenfeld-Lieberthal & Daniel Czamanski, 2006. "The Dynamics of the Tel Aviv Morphology," Environment and Planning B, , vol. 33(2), pages 269-284, April.
    14. 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.
    15. Song, Zhijun & Jin, Wenxuan & Jiang, Guanghui & Li, Sichun & Ma, Wenqiu, 2021. "Typical and atypical multifractal systems of urban spaces—using construction land in Zhengzhou from 1988 to 2015 as an example," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    16. Huan Lu & Ruiyang Wang & Rong Ye & Jinzhao Fan, 2023. "Monitoring Long-Term Spatiotemporal Dynamics of Urban Expansion Using Multisource Remote Sensing Images and Historical Maps: A Case Study of Hangzhou, China," Land, MDPI, vol. 12(1), pages 1-23, January.
    17. Myagmartseren Purevtseren & Bazarkhand Tsegmid & Myagmarjav Indra & Munkhnaran Sugar, 2018. "The Fractal Geometry of Urban Land Use: The Case of Ulaanbaatar City, Mongolia," Land, MDPI, vol. 7(2), pages 1-14, May.
    18. Chen, Yanguang, 2013. "Fractal analytical approach of urban form based on spatial correlation function," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 47-60.
    19. Czamanski, Daniel & Broitman, Dani, 2017. "Information and communication technology and the spatial evolution of mature cities," Socio-Economic Planning Sciences, Elsevier, vol. 58(C), pages 30-38.
    20. Chen, Yanguang & Jiang, Shiguo, 2009. "An analytical process of the spatio-temporal evolution of urban systems based on allometric and fractal ideas," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 49-64.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:envirb:v:33:y:2006:i:3:p:345-364. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.