Morphological similarities between DBM and an economic geography model of city growth

An urban microeconomic model of households evolving in a 2D cellular automata allows to simulate the growth of a metropolitan area where land is devoted to housing, road network and agricultural/green areas. This system is self-organised: based on individualistic decisions of economic agents who compete on the land market, the model generates a metropolitan area with houses, roads, and agriculture. Several simulation are performed. The results show strong similarities with physical Dieletric breakdown models (DBM). In particular, phase transitions in the urban morphology occur when a control parameter reaches critical values. Population density in our model and the electric potential in DBM play similar roles, which can explain these resemblances.