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.
International audienceIn this paper we extract the morphological boundaries of urban agglomerations and characterize boundary shapes using eight fractal and nonfractal spatial indexes. Analyses were first performed on six archetypal theoretical cities, and then on Belgium's 18 largest towns. The results show that: (1) the relationship between the shape of the urban boundary (fractal dimension, dendricity, and compactness) and the built morphology within the urban agglomeration (fractal dimension, proportion of buildings close to the urban boundary) is not straightforward; (2) each city is a unique combination of the morphological characteristics considered here; (3) due to their different morphological characteristics, the planning potential of Flemish and Walloon cities seems to be very different
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