Modeling large Mexican urban metropolitan areas by a Vicsek Szalay approach

A modified Vicsek–Szalay model is introduced. From this, experiments are performed in order to simulate the spatial morphology of the largest metropolitan area of México: a set of clusters formed by the Valle de México metropolitan area (VMMA), Puebla metropolitan area (PMA) and Toluca metropolitan area (TMA). This case is presented in detail and here is called the Central México metropolitan area (CMMA). To verify the effectiveness of our approach we study two other cases; the set of clusters formed by the Monterrey zone (MZ, formed by the Monterrey metropolitan area and the Saltillo City metropolitan area) and the Chihuahua zone (ChZ, formed by the Chihuahua metropolitan area, Delicias City and Cuauthemoc City ), with acceptable results. Besides we compute three different fractal measures for all our areas of interest (AOI). In this paper, we focus on the global feature of these fractal measures in the description of urban geography and obtained local information which normally comes from inner city structures and small scale human decisions. Finally, we verified that the Zipf law is fulfilled by our simulated urban morphologies, so we know that our model follows it. As is normal for actual city size distributions, the CMMA case is presented in detail. We intend to pave the way in the understanding of population spatial distribution in a geographical space.