Patterns of City Formation and Development

Cities are complex entities, which escape simplistic description. The formulation of mathematical laws governing the evolution of cities has recently been a hot topic, ignited by the publication of Geoffrey West's Scaling law, which claims to explain why people flock to cities in terms of enhanced productivity and environmental efficiency. But West's work remains highly controversial for its non-universal applicability, and its failure to grasp more recent phenomena of flourishing suburban economies.
In an attempt to better understand how cities emerge and develop, this project looks at possible ways to study the complexity of city networks and their evolution in time. We aim to expose further insights towards the identification of mathematical laws governing the evolution of cities.
We will begin the research by refining existing models of cities emergence using a parent Poisson cluster process to model their appearance and a daughter Poisson cluster process to capture their physical spread. The first step will therefore be that of finding a sensible measure of the entropy (i.e. the complexity) of the resulting network, considering both the distance between cities and their sprawl. A further step is to consider the time evolution of this network, comparing values of the entropy for different time-steps to understand its evolution as cities change, multiply and interact.
We believe that this will inform policies that aim to deal with urban growth and development.

Alignment with EPSRC research themes: Infrastructure and Urban Systems; Complexity Science.