Fractal geometry and urban patterns – from exploring morphology to applications in planning

International audienceFractal geometry turned out to be a powerful approach in many domains for describing complex structures which have multiscale properties. In particular, fractal analysis allows making evident scaling properties and hence underlying structural order principles which cannot be discovered by other measuring approaches like densities which refer to one unique scale. We present here how this approach helps to analyze the distribution of build-up surface in urban patterns and how it can be used to link these morphologiocal properties to specific contexts of urbanization. Indeed, contemporary urban patterns have usually an irregular shape reminding rather deposits on surfaces or corrosive phenomena. This can be explained by the fact that urban growth is nowadays often a weakly controlled process where a couple of agents interact on different scales. Hence urbanization can be seen as selforganization process. Nevertheless it can be surprising that these interactions generate structures which follow obviously underlying order principle. In contrast there exist, too, urban planning concepts, which follow scaling principles by definition, what allows reflecting on elements to what extend such patterns correspond to optimization principles. We start by introducing fractal models which illustrate how fractals can be linked to urban patterns. Then we introduce the measuring methods used and we discuss the results obtained. In a last part we show a possible link to the order parameter concept used in synergetics and we finish by giving an outlook how the fractal approach can be useful for developing planning concepts in the sense of optimization