Fractal geometry of urban patterns and their morphogenesis

Abstract

URBAN PATTERN FORMATION SOME PRELIMINARY REMARKS One of the most striking features of urban dynamics is the emergence of highly irregular settlement patterns which are often perceived as amorphous. Urban planning deplores this evolution which turns out to be hardly controlable. Indeed the settlement dynamics is the result of complex socioeconomic interaction processes including several levels of organization. On a microlevel, agents take decisions for constructing dwellings, shopping centers, manufactories, etc. Thus the settlement dynamics appears as a discrete process in time which should rather be interpreted as a random-like sequence of decisions. However these decisions are not taken in an independent way. On the one hand, there exist static physical constraints like mountain barriers, etc., on the other hand, planning policy defines the legal framework of settlement dynamics but guarantees also the construction and maintenance of infrastructure. In order to have an impact on planning decisions, agents organize themselves eventually in pressure groups with diverging aspirations. Moreover due to the expansion of cities, an increasing 127 number of municipalities and other administrations are involved in these decisions and there exists a competition between different types of decision makers. Nevertheless, despite of the complexity of the processes which contribute to the morphogenesis of these patterns and despite of their irregular form, they show some typical features like dendritic branches which grow along the transportation axes. Obviously this type of evolution seems to be a widespread phenomenon, which is even observed in countries with a centralistic planning policy. This inspires to interpret urban pattern formation, from a synergetic point of view, as a self-organization process where complex dynamics generates a certain type of spatial organization. In order to analyze and to modelize this pattern formation, we should dispose of measures which allow to make evident their spatial organization. Indeed, a good knowledge about the urban morphology seems to be crucial for developing an "urban metric" in order to verify to what extend patterns simulated by some dynamic models are in concordance with real world patterns. Traditional measures, used in urban planning, based on the notion of density, seem not to be