A model of the spatiotemporal evolution of urban areas is developed that simultaneously includes the effects on household utility of geography, population density, income distribution, and household preference for characteristics of dwellings and neighbors. The result is a utility function whose structure is similar to that of the energy of interacting spin systems in external fields. Spatiotemporal housing market evolution then results via transactions driven by increases in utility and changes in numbers of households and dwellings. It is shown that the model successfully predicts formation of monocentric and polycentric urban areas, stratification by wealth, segregation due to preferences for housing or neighbors, and the balance of supply and demand. These results go well beyond those of prior models that each dealt with subsets of these phenomena, and do so within a single, unified framework. Potential generalizations are discussed and further applications are suggested.
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