Dynamics of Cities

TL;DR

This paper applies a nonextensive diffusion model to analyze city dynamics, revealing how fractal dimensions relate to urban scaling and social interactions, thereby enhancing understanding of urban evolution.

Contribution

It introduces a nonextensive diffusion approach to connect fractal city properties with urban scaling and social behavior, advancing urban complexity modeling.

Findings

Fractal dimension correlates with the entropic index q.

Urban scaling exponents relate to fractal measures.

Model effectively captures stationary urban phases.

Abstract

This study investigates city dynamics employing a nonextensive diffusion equation suited for addressing diffusion within a fractal medium, where the nonadditive parameter, $q$, plays a relevant role. The findings demonstrate the efficacy of this approach in determining the relation between the fractal dimension of the city, the allometric exponent and $q$, and elucidating the stationary phase of urban evolution. The dynamic methodology facilitates the correlation of the fractal dimension with both the entropic index and the urban scaling exponent identified in data analyses. The results reveal that the scaling behaviour observed in cities aligns with the fractal dimension measured through independent methods. Moreover, the interpretation of these findings underscores the intimate connection between the fractal dimension and social interactions within the urban context. This research contributes to a deeper comprehension of the intricate interplay between human behaviour, urban dynamics, and the underlying fractal nature of cities.