Fractal geometry for analyzing and modeling urban patterns and planning sustainable cities

The dynamics of agglomerations are influenced by a great number of individual and collective decisions made by different types of actors. These socio-economic processes act on different scales of space and time, which is typical for complex systems dynamics. The emerging urban patterns have often been seen as amorphous, devoid of any apparent order. However, it turns out that the cross-scale approach of fractal geometry provides a better understanding of their spatial organization. The morphological properties of urban patterns can be illustrated by fractal reference models. Moreover, the fractal properties of those patterns can be linked to historical contexts or planning concepts. In some sense, fractal parameters could be construed as a kind of order parameter, describing the pattern of organization on a macro-scale without us having full knowledge of the role of the different underlying socio-economic processes. We may then reflect on the extent to which the observed macro-scale organization corresponds in some way to a general self-optimizing principle. In this context economic modeling proves useful. This leads us to discuss a planning concept based on fractal geometry designed to contribute to sustainable urban development.