This paper presents a quasi-3D cellular automaton (CA) simulation model of cities. A 2D CA model includes a cell attribute that represents building height information. Dynamic processes are depicted using four parameters: initial building coverage, interaction with adjacent neighborhood, inertia, and noise. These parameters can assume simple economic interpretation. Some combinations of values of the parameters result in cities that experience paths of convergent growth. Some values lead to cities that experience phase transitions. We suggest a typology of resulting urban patterns and note the emergence of spatial clusters of high-rise buildings.