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Fractal dimension versus density of built‐up surfaces in the periphery of Brussels

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  • Isabelle Thomas
  • Pierre Frankhauser
  • Marie‐Laurence De Keersmaecker

Abstract

. This paper tries to demonstrate the usefulness of a fractal analysis for characterising the morphology of built‐up areas within the peri‐urban fringe. Methodology and expectations are discussed theoretically and geometrically. An empirical analysis is then performed on the southern periphery of Brussels. The effect of the size and shape of the windows is evaluated; this leads to a methodological discussion about the real meaning of fractality and its relationship to density. These analyses confirm the usefulness and limits of the fractal approach: it is a promising tool for describing the morphology of cities and for simulating the growth and development of this field of research. Abstract. Este artículo pretende demostrar la utilidad de un análisis fractal para caracterizar la morfología de áreas urbanizadas dentro del área peri urbana. La metodología y expectativas se discuten teórica y geométricamente. A continuación se realiza un análisis empírico en la periferia del sur de Bruselas. Se evalúa el efecto del tamaño y forma de las ventanas; esto lleva a una discusión metodológica sobre el verdadero significado de la fractalidad y su relación con la densidad. Estos análisis confirman la utilidad y limites del enfoque fractal: Es una herramienta promisoria para describir la morfología de ciudades y para simular el crecimiento y desarrollo de este campo de investigación.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:presci:v:86:y:2007:i:2:p:287-308
    DOI: 10.1111/j.1435-5957.2007.00122.x
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    References listed on IDEAS

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    1. Alex Anas & Richard Arnott & Kenneth A. Small, 1998. "Urban Spatial Structure," Journal of Economic Literature, American Economic Association, vol. 36(3), pages 1426-1464, September.
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    Cited by:

    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. 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.
    3. 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.
    4. 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.
    5. Chen, Yanguang, 2012. "Fractal dimension evolution and spatial replacement dynamics of urban growth," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 115-124.
    6. 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.
    7. 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.
    8. Dekolo, Samuel & Oduwaye, Leke & Nwokoro, Immaculata, 2016. "Urban Sprawl and Loss of Agricultural Land in Peri-urban Areas of Lagos," MPRA Paper 73726, University Library of Munich, Germany.
    9. Francisco Martínez & Bastian Sepúlveda & Hermann Manríquez, 2023. "Fractal Organization of Chilean Cities: Observations from a Developing Country," Land, MDPI, vol. 12(2), pages 1-21, January.
    10. Chen, Yanguang, 2013. "Fractal analytical approach of urban form based on spatial correlation function," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 47-60.
    11. 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.
    12. 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.
    13. Pavel Em, 2014. "The Concept of Fuzzy Central Place as the Approach to Analyze Distribution of Central Functions within Urban Agglomerations," ERSA conference papers ersa14p212, European Regional Science Association.
    14. 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.
    15. 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.
    16. Fatih Terzi & H Serdar Kaya, 2011. "Dynamic Spatial Analysis of Urban Sprawl through Fractal Geometry: The Case of Istanbul," Environment and Planning B, , vol. 38(1), pages 175-190, February.
    17. 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.
    18. 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).
    19. 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.
    20. 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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