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Clustering Patterns of Urban Built-up Areas with Curves of Fractal Scaling Behaviour

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  • Isabelle Thomas

    (FRS-FNRS, CORE, and Department of Geography, Université catholique de Louvain, Voie du Roman Pays, 34 B-1348, Louvain-la-Neuve, Belgium)

  • Pierre Frankhauser

    (THEMA (CNRS UMR 6049), Université de Franche-Comté, Besançon, France)

  • Benoit Frenay

    (Machine Learning Group, Université catholique de Louvain, Louvain-la-Neuve, Belgium)

  • Michel Verleysen

    (Machine Learning Group, Université catholique de Louvain, Louvain-la-Neuve, Belgium; and SAMOS-MATISSE, Université Paris 1 Panthéon-Sorbonne, Paris, France)

Abstract

Fractal dimension is an index which can be used to characterize urban areas. The use of the curve of scaling behaviour is less common. However, its shape gives local information about the morphology of the built-up area. This paper suggests a method based on a k -medoid for clustering these curves. It is applied to forty-nine wards of European cities, and shows that the curves add interesting intraward information to our knowledge of the spatial variation of the urban texture. Moreover, morphological similarities are observed between cities: living, architectural, and planning trends are not specific to individual cities.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:envirb:v:37:y:2010:i:5:p:942-954
    DOI: 10.1068/b36039
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    References listed on IDEAS

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    1. 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.
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    1. Isabelle Thomas & Pierre Frankhauser, 2013. "Fractal Dimensions of the Built-up Footprint: Buildings versus Roads. Fractal Evidence from Antwerp (Belgium)," Environment and Planning B, , vol. 40(2), pages 310-329, April.
    2. Athanasios Votsis, 2017. "Exploring the spatiotemporal behavior of Helsinki’s housing prices with fractal geometry and co-integration," Journal of Geographical Systems, Springer, vol. 19(2), pages 133-155, April.
    3. 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).
    4. Chen, Yanguang, 2013. "Fractal analytical approach of urban form based on spatial correlation function," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 47-60.
    5. 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.
    6. Mikhail Kanevski, 2021. "Unsupervised learning of Swiss population spatial distribution," PLOS ONE, Public Library of Science, vol. 16(2), pages 1-24, February.
    7. Janka Lengyel & Seraphim Alvanides & Jan Friedrich, 2023. "Modelling the interdependence of spatial scales in urban systems," Environment and Planning B, , vol. 50(1), pages 182-197, January.
    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. 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).
    12. Chen, Yanguang, 2012. "Fractal dimension evolution and spatial replacement dynamics of urban growth," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 115-124.
    13. Claudia Yamu & Gert de Roo & Pierre Frankhauser, 2016. "Assuming it is all about conditions. Framing a simulation model for complex, adaptive urban space," Environment and Planning B, , vol. 43(6), pages 1019-1039, November.
    14. Chen, Yanguang, 2022. "Normalizing and classifying shape indexes of cities by ideas from fractals," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    15. 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.

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