IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v49y2013icp47-60.html
   My bibliography  Save this article

Fractal analytical approach of urban form based on spatial correlation function

Author

Listed:
  • Chen, Yanguang

Abstract

Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities are not yet revealed in theory. By mathematical deduction and transform (e.g., Fourier transform), I find that scaling analysis, spectral analysis, and spatial correlation analysis are all associated with fractal concepts and can be integrated into a new approach to fractal analysis of cities. This method can be termed ‘3S analyses’ of urban form. Using the 3S analysis, I derived a set of fractal parameter equations, by which different fractal parameters of cities can be linked up with one another. Each fractal parameter has its own reasonable extent of values. According to the fractal parameter equations, the intersection of the rational ranges of different fractal parameters suggests the proper scale of the fractal dimension of urban patterns, which varies from 1.5 to 2. The fractal dimension equations based on the 3S analysis and the numerical relationships between different fractal parameters are useful for geographers to understand urban evolution and potentially helpful for future city planning.

Suggested Citation

  • Chen, Yanguang, 2013. "Fractal analytical approach of urban form based on spatial correlation function," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 47-60.
    • Handle: RePEc:eee:chsofr:v:49:y:2013:i:c:p:47-60
    DOI: 10.1016/j.chaos.2013.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077913000349
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2013.02.006?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. repec:cai:popine:popu_p1998_10n1_0240 is not listed on IDEAS
    3. Yanguang Chen, 2010. "Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-20, December.
    4. 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.
    5. 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.
    6. Chen, Yanguang, 2009. "Urban gravity model based on cross-correlation function and Fourier analyses of spatio-temporal process," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 603-614.
    7. Isabelle Thomas & Pierre Frankhauser & Benoit Frenay & Michel Verleysen, 2010. "Clustering Patterns of Urban Built-up Areas with Curves of Fractal Scaling Behaviour," Environment and Planning B, , vol. 37(5), pages 942-954, October.
    8. Isabelle Thomas & Pierre Frankhauser & Marie‐Laurence De Keersmaecker, 2007. "Fractal dimension versus density of built‐up surfaces in the periphery of Brussels," Papers in Regional Science, Wiley Blackwell, vol. 86(2), pages 287-308, June.
    9. Chen, Yanguang, 2012. "Fractal dimension evolution and spatial replacement dynamics of urban growth," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 115-124.
    10. Isabelle Thomas & Marie-Laurence De Keersmaecker & Pierre Frankhauser, 2003. "Using fractal dimensions for characterizing intra-urban diversity. The example of Brussels," ERSA conference papers ersa03p116, European Regional Science Association.
    11. Yanguang Chen, 2011. "Modeling Fractal Structure of City-Size Distributions Using Correlation Functions," PLOS ONE, Public Library of Science, vol. 6(9), pages 1-9, September.
    12. Michael Batty & Yichun Xie, 1999. "Self-organized criticality and urban development," Discrete Dynamics in Nature and Society, Hindawi, vol. 3, pages 1-16, January.
    13. Yanguang Chen & Shiguo Jiang, 2010. "Modeling Fractal Structure of Systems of Cities Using Spatial Correlation Function," International Journal of Artificial Life Research (IJALR), IGI Global, vol. 1(1), pages 12-34, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Man, Wang & Nie, Qin & Li, Zongmei & Li, Hui & Wu, Xuewen, 2019. "Using fractals and multifractals to characterize the spatiotemporal pattern of impervious surfaces in a coastal city: Xiamen, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 44-53.
    2. Estelle Mennicken & Rémi Lemoy & Geoffrey Caruso, 2024. "Road network distances and detours in Europe: Radial profiles and city size effects," Environment and Planning B, , vol. 51(1), pages 174-194, January.
    3. Yanguang Chen, 2015. "A New Methodology of Spatial Cross-Correlation Analysis," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-20, May.
    4. DELLOYE, Justin & LEMOY, Rémi & CARUSO, Geoffrey, 2017. "Alonso and the scaling of urban profiles," LIDAM Discussion Papers CORE 2017037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Yanguang Chen, 2021. "An analytical process of spatial autocorrelation functions based on Moran’s index," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-27, April.
    6. Li, Huanhuan & Xu, Beibei & Riasi, Alireza & Szulc, Przemyslaw & Chen, Diyi & M'zoughi, Fares & Skjelbred, Hans Ivar & Kong, Jiehong & Tazraei, Pedram, 2019. "Performance evaluation in enabling safety for a hydropower generation system," Renewable Energy, Elsevier, vol. 143(C), pages 1628-1642.
    7. Haosu Zhao & Bart Julien Dewancker & Feng Hua & Junping He & Weijun Gao, 2020. "Restrictions of Historical Tissues on Urban Growth, Self-Sustaining Agglomeration in Walled Cities of Chinese Origin," Sustainability, MDPI, vol. 12(14), pages 1-29, July.
    8. Chen, Yanguang, 2013. "A set of formulae on fractal dimension relations and its application to urban form," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 150-158.
    9. Chen, Yanguang & Wang, Yihan & Li, Xijing, 2019. "Fractal dimensions derived from spatial allometric scaling of urban form," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 122-134.
    10. Fatemeh Jahanmiri & Dawn Cassandra Parker, 2022. "An Overview of Fractal Geometry Applied to Urban Planning," Land, MDPI, vol. 11(4), pages 1-23, March.
    11. Chen, Yanguang, 2017. "Multi-scaling allometric analysis for urban and regional development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 673-689.
    12. Lang, Wei & Long, Ying & Chen, Tingting & Li, Xun, 2019. "Reinvestigating China’s urbanization through the lens of allometric scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1429-1439.
    13. Xu, Beibei & Chen, Diyi & Zhang, Hao & Wang, Feifei, 2015. "Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 50-61.

    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, 2013. "A set of formulae on fractal dimension relations and its application to urban form," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 150-158.
    2. Chen, Yanguang, 2012. "Fractal dimension evolution and spatial replacement dynamics of urban growth," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 115-124.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. Chen, Yanguang & Lin, Jingyi, 2009. "Modeling the self-affine structure and optimization conditions of city systems using the idea from fractals," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 615-629.
    9. Isabelle Thomas & Pierre Frankhauser & Dominique Badariotti, 2012. "Comparing the fractality of European urban neighbourhoods: do national contexts matter?," Journal of Geographical Systems, Springer, vol. 14(2), pages 189-208, April.
    10. Jian Feng & Yanguang Chen, 2010. "Spatiotemporal Evolution of Urban Form and Land-Use Structure in Hangzhou, China: Evidence from Fractals," Environment and Planning B, , vol. 37(5), pages 838-856, October.
    11. Chen, Yanguang, 2011. "Fractal systems of central places based on intermittency of space-filling," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 619-632.
    12. 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.
    13. Chen, Yanguang & Feng, Jian, 2012. "Fractal-based exponential distribution of urban density and self-affine fractal forms of cities," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1404-1416.
    14. Chen, Yanguang, 2022. "Normalizing and classifying shape indexes of cities by ideas from fractals," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    15. Saeedimoghaddam, Mahmoud & Stepinski, T.F. & Dmowska, Anna, 2020. "Rényi’s spectra of urban form for different modalities of input data," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    16. Chen, Yanguang & Huang, Linshan, 2019. "Modeling growth curve of fractal dimension of urban form of Beijing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1038-1056.
    17. Cécile Tannier & Gilles Vuidel & Hélène Houot & Pierre Frankhauser, 2012. "Spatial Accessibility to Amenities in Fractal and Nonfractal Urban Patterns," Environment and Planning B, , vol. 39(5), pages 801-819, October.
    18. Chong Zhao & Yu Li & Min Weng, 2021. "A Fractal Approach to Urban Boundary Delineation Based on Raster Land Use Maps: A Case of Shanghai, China," Land, MDPI, vol. 10(9), pages 1-21, September.
    19. Chen, Yanguang, 2014. "An allometric scaling relation based on logistic growth of cities," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 65-77.
    20. 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.

    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:eee:chsofr:v:49:y:2013:i:c:p:47-60. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.