A fractal approach to identifying urban boundaries

Cécile Tannier (1) , Isabelle Thomas (2) , Gilles Vuidel (1) , Pierre Frankhauser (1)

1 ThéMA - Théoriser et modéliser pour aménager (UMR 6049)
2 CORE and Department of Geography

Fractal geometry can be used for determining the morphological boundaries of metropolitan areas. A two-step method is proposed here: (1) Minkowski's dilation is applied to detect any multiscale spatial discontinuity and (2) a distance threshold is located on the dilation curve corresponding to a major change in its behavior. We therefore measure the maximum curvature of the dilation curve. The method is tested on theoretical urban patterns and on several European cities to identify their morphological boundaries and to track boundary changes over space and time. Results obtained show that cities characterized by comparable global densities may exhibit different distance thresholds. The less the distances separating buildings differ between an urban agglomeration and its surrounding built landscape, the greater the distance threshold. The fewer the buildings that are connected across scales, the greater the distance threshold.

Mots clés: urban boundaries; fractal approach

Domaines: Géographie

Cécile Tannier, Isabelle Thomas, Gilles Vuidel, Pierre Frankhauser. A fractal approach to identifying urban boundaries. Geographical Analysis, 2011, 43 (2), pp.211-227. ⟨10.1111/j.1538-4632.2011.00814.x⟩. ⟨hal-00731648⟩