Discrete Dynamics in Nature and Society
Volume 3 (1999), Issue 2-3, Pages 137-147

From fast to slow processes in the evolution of urban and regional settlement structures

Wolfgang Weidlich

Institute of Theoretical Physics, University of Stuttgart, Pfaffenwaldring 57/111, Stuttgart D-70550, Germany

Received 16 November 1998

Copyright © 1999 Wolfgang Weidlich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Complex systems consist of many intertwined organizational levels starting from micro-structures and ending with macrostructures. Their evolution takes place on different time scales: Micropatterns exhibit a fast dynamics whereas macropatterns develop slowly. Urban and regional science can make use of this fact by constructing a hierarchy of models on different spatio-temporal scales.

Based on this understanding two models are presented: One for the relatively fast urban evolution on the microscale and one for the relatively slow regional evolution on the macroscale.

The micromodel considers the urban structure as a system of sites on which different kinds of buildings (dwellings, schools, stores, service-stations, factories ... ) can be erected. The step by step evolution of the city configuration is treated as a stochastic process guided by desirability considerations. The formalization of this concept leads to equations for the evolution of the urban city configuration. Numerical simulations illustrate this urban “microdynamics”.

The macromodel treats the settlement formation in a region on a more global scale. The evolution of the density of economically active populations who produce and consume goods is considered. The driving force of density changes is the spatial difference of incomes motivating the individuals to migrate to locations of optimal income. This nonlinear process leads to the self-organization of spatially heterogeneous population distributions forming the settlements. Their micro-structure can thereupon be treated by the micromodel.