Cities and fractals: simulating growth and form

The morphology of cities bears an uncanny resemblance to those dendritic clusters of particles which have been recently simulated as fractal growth processes. This paper explores this analogy, first presenting both deterministic and stochastic models of fractal growth, and then suggesting how these models might form an appropriate baseline for models of urban growth. In particular, the diffusion-limited aggregation (DLA) and dielectric breakdown models (DEM) are outlined, and comparisons are made between simulated clusters and the form of medium-sized towns. Using the DBM formulation, constraints and distortions on the simulated clusters are illustrated, thus enabling the model to simulate a continuum of cluster forms from the one- to the two-dimensional. This model is then applied to the town of Cardiff, UK, and a critical evaluation of its performance is used to identify future research.