Modeling Urban Growth Patterns with Correlated Percolation
  We propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. The model is also consistent with observable urban growth dynamics, our results agreeing both qualitatively and quantitatively with urban data. The resulting growth morphology can be understood from interactions among the constituent units forming an urban region, and can be modeled using a correlated percolation model in the presence of a gradient. 
Hernan A. Makse (BU), Jose S. Andrade Jr. (UFC, Brazil), Michael Batty   (Univ. College London), Shlomo Havlin (Bar-Ilan), a...