Summary: Urban centers present all over the world striking similarities which translate into universal laws describing their growth and morphology. In this paper, we study a simple two-dimensional cellular automata model containing what we identify as essential ingredients in the demographic change. The slow addition of population to an initially empty area (mimicking migration) added with a reaction diffusion process (representing reorganization of the population) allow us to recover many real data and provide us with a better understanding of the main processes forming and shaping the modern metropolis.