Fractal geometry for measuring and modelling urban patterns

Urban growth generates nowadays patterns, which look rather irregular. Planning policy regrets the lack of compactness and density of these agglomerations, but controlling urban sprawl turns out to be difficult. Obviously a new type of spatial organisation emerges, which is rather the result of a self-organisation process to which a high number of social agents contribute. In the present contribution we focus on the use of fractal geometry which turned out to be a powerful instrument for describing the morphology of these patterns. After an introduction about the context of research, fractal models are presented, which serve as reference models for better understanding the spatial organisation of settlement patterns. Then the methodology for measuring their morphology by means of fractal parameters is explained. Moreover different peculiar topics are considered like a specific approach of urban boundaries. Then an overview is given over results obtained for a couple of agglomerations in different European countries. The interpretation of these results allows establishing links between urban planning policy and pattern morphology. Applying the idea of self-organisation leads to introducing a fractal order parameter for studying the emergent fractal order in urban patterns. The presentation of these quantitative results will be completed by some reflections about how planning concepts based on fractal geometry may help to manage more efficiently urban sprawl