Revealing configurational attractors in the evolution of modern Australian and US cities

The spatial structure of modern cities exhibits highly diverse patterns and keeps evolving under numerous constraints and sustainability demands. However, it is unclear if there are fundamental physical constraints guiding the evolution of cities. Here, we offer a concise model revealing key invariants within urban forms shaped by human resettlement over the years. In doing so, we assess the heterogeneity and spreading of population density in 25 Australian and 175 US cities. We observe that larger cities tend to form a cluster with low spreading and high heterogeneity, and explain this observation using dynamic properties of the intra-urban migration in these cities. As a result, we report three distinct feasible phases of urban structures: uniform, monocentric, and polycentric, separated by abrupt regime shifts. We demonstrate that transitions between these phases, resulting from the population redistribution, are not necessarily driven by external factors (such as city growth) and can exist even in a closed system. Our analysis reveals that the set of all possible equilibrium configurations (“configurational attractors”) form a narrow region in the heterogeneityspreading space, thus explaining the emergence of clustering patterns.