Two-dimensional cellular automata with rules defined on a large neighbourhood are used to simulate the evolution of urban land-use patterns. Both the simulated urban areas and actual cities are shown to be fractal objects characterized by very similar dimensions. But the fractality (and hence realism) of the cellular cities appears only when the degree of stochasticity is within a relatively narrow band; otherwise the city is too uniform or too random. The same phenomenon appears in a conventional dynamic model of the evolution of a system of cities: the size distribution of urban centres assumes a fractal form (one observed in many real systems) only with a ‘fine tuning’ of the relevant parameters. Otherwise the system either evolves toward a uniform state or collapses to a single large centre. The tendency to observe such poised behaviour in both the cellular and the urban system models for realistic calibrations may be a manifestation of a phase-transition phenomenon observed in simpler deterministic cellular automata, and may represent a requirement for evolvability in real systems.