The geometric origins of complex cities

Abstract

Due to the rapid urbanization, cities have become a hot topic. Extensive complex phenomena, such as scaling laws with respect to population, morphology, spatial distribution within cities have been revealed and validated by the empirical studies. Yet there’s still no clear answer to the question that what’s the underlying mechanism responsible for these observed complex phenomena. Most of previous studies only focus on one aspect of the city. However, focusing on only one aspect may lose the whole picture of it. Based on a very simple “matching growth” rule and two more simple assumptions, which are all performed locally, we propose a simple model which can derive most of observed macro scaling relations and spatial distribution. All these theoretical deductions can be well supported by empirical data. And the consistency between the exponents of different cumulative spatial distribution may indicates that the city really follows the rules we assumed.