Modeling Urban Morphology by Unifying Diffusion-Limited Aggregation and Stochastic Gravitation

More than 30 years ago, Diffusion-Limited Aggregation (DLA) has been studied as mechanism to generate structures sharing similarities with real-world cities. Recently, a stochastic gravitation model (SGM) has been proposed for the same purpose but representing a completely different mechanism. Both approaches have advantages and disadvantages, while e.g. the dendrites emerging via DLA are visually very different from real-world cities, the SGM does not preserve undeveloped locations close to the city center. Here we propose a unification of both mechanisms, i.e. a particle moves randomly and turns into an urban site with a probability that depends on the proximity to already developed sites. We study the cluster size distributions of the structures generated by both models and find that SGM generates more balanced distributions. We also propose a way to assess to which extent the largest cluster is a primate city and find that in both models, beyond certain parameter value, the size of the largest cluster becomes inconsistent with being drawn from the same distribution of remaining clusters.