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 2-dimensional cellular automata model containing what we identfiy as essential ingredients in the dimographic change. the slow addition of population to an initially empty area (mimicking migration) added with a reaction-diffusion process (representing reorganization of the population) allows us to recover many real data and provide us with a better understanding of the main processes forming and shaping the modern metropolis. Submitted to Fractals.