From complex structures to complex processes: Percolation theory applied to the formation of a city

We investigate the morphology of the spatial pattern resulting from the division of land into the parcels that is observed in the centers of the cities, by analyzing the distribution function of the parcel areas. A simple model based on a two-dimensional bond percolation is employed to mimic the process of the formation of the city. The model reproduces the empirical distribution of the parcel areas that is found to exhibit the power law with the exponent tau=2.0. We argue that the city emerges from a collection of separated settlements in a process that can be described as a structural phase transition.