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Using fractal dimensions for characterizing intra-urban diversity: the example of Brussels

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  • DE KEERSMAECKER, Marie-Laurence
  • FRANKHAUSER, Pierre
  • THOMAS, Isabelle

Abstract

The objective of this paper is to compare fractal-based parameters calculated by different fractal methods for urban built-up areas, and to link the observed spatial variations to variables commonly used in urban geography, urban economics or land use planning. Computations are performed on Brussels. Two fractal methods (correlation and dilation) are systematically applied for evaluating the fractal dimension of built-up surfaces; correlation is used to evaluate the fractal dimension of the borders (lines). Analyses show that while fractal dimension is ideal for distinguishing the morphology of Brussels, each estimation technique leads to slightly different results. Interesting associations are to be found between the fractal dimensions and rent, distance, income and planning rules. Despite its limitations, fractal analysis seems to be a promising tool for describing the morphology of the city and for simulating its genesis and planning. The model is robust: it replicates the urban spatial regularities and patterns, and could hence fruitfully be integrated into intra urban simulation processes.
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Suggested Citation

  • DE KEERSMAECKER, Marie-Laurence & FRANKHAUSER, Pierre & THOMAS, Isabelle, 2003. "Using fractal dimensions for characterizing intra-urban diversity: the example of Brussels," LIDAM Reprints CORE 1686, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:1686
    DOI: 10.1111/j.1538-4632.2003.tb01117.x
    Note: In : Geographical Analysis, 35(4), 310-328, 2003
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    Cited by:

    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. Jean Cavailhès & Pierre Frankhauser & Dominique Peeters & Isabelle Thomas, 2010. "Residential equilibrium in a multifractal metropolitan area," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 45(3), pages 681-704, December.
    3. Stepinski, Tomasz F. & Dmowska, Anna, 2020. "Complexity in patterns of racial segregation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Blaudin de Thé, Camille & Carantino, Benjamin & Lafourcade, Miren, 2021. "The carbon ‘carprint’ of urbanization: New evidence from French cities," Regional Science and Urban Economics, Elsevier, vol. 89(C).
    5. 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.
    6. Szymon Czyża & Karol Szuniewicz & Iwona Cieślak & Andrzej Biłozor & Tomasz Bajerowski, 2023. "An Analysis of the Spatial Development of European Cities Based on Their Geometry and the CORINE Land Cover (CLC) Database," IJERPH, MDPI, vol. 20(3), pages 1-21, January.
    7. 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).
    8. Chen, Yanguang, 2013. "Fractal analytical approach of urban form based on spatial correlation function," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 47-60.
    9. 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.
    10. 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.
    11. Lafourcade, Miren & Blaudin de Thé, Camille & Carantino, Benjamin, 2018. "The Carbon `Carprint' of Suburbanization: New Evidence from French Cities," CEPR Discussion Papers 13086, C.E.P.R. Discussion Papers.
    12. Marianne Guérois & Denise Pumain, 2008. "Built-Up Encroachment and the Urban Field: A Comparison of Forty European Cities," Environment and Planning A, , vol. 40(9), pages 2186-2203, September.
    13. 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.
    14. Saeedimoghaddam, Mahmoud & Stepinski, T.F., 2021. "Multiplicative random cascade models of multifractal urban structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    15. Chen, Yanguang, 2012. "Fractal dimension evolution and spatial replacement dynamics of urban growth," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 115-124.
    16. 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.
    17. Chen, Yanguang, 2022. "Normalizing and classifying shape indexes of cities by ideas from fractals," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    18. Adam, Arnaud & Finance, Olivier & Thomas, Isabelle, 2021. "Monitoring trucks to reveal Belgian geographical structures and dynamics: From GPS traces to spatial interactions," Journal of Transport Geography, Elsevier, vol. 91(C).
    19. 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.
    20. 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.
    21. 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.
    22. Zhonghao Zhang & Rui Xiao & Weixuan Yu & Yue Liu & Meng Lin & Meng Wang, 2017. "Characterizing Factors Associated with Built-Up Land Expansion in Urban and Non-Urban Areas from a Morphological Perspective," Sustainability, MDPI, vol. 9(8), pages 1-15, August.
    23. 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.

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