Cities and Regions in Britain through hierarchical percolation

TL;DR

This paper uses hierarchical percolation on street networks to reveal multi-scale urban and regional structures in Britain, aligning with known boundaries and divisions, and analyzing their morphological evolution.

Contribution

It introduces a novel application of percolation theory to uncover hierarchical urban and regional structures at multiple scales in Britain.

Findings

Hierarchical structures correspond to natural and social boundaries.

Percolation clusters match satellite and population-based city boundaries.

Fractal dimension analysis reveals morphological evolution of urban clusters.

Abstract

Urban systems present hierarchical structures at many different scales. These are observed as administrative regional delimitations which are the outcome of complex geographical, political and historical processes which leave almost indelible footprints on infrastructure such as the street network. In this work we uncover a set of hierarchies in Britain at different scales using percolation theory on the street network and on its intersections which are the primary points of interaction and urban agglomeration. At the larger scales, the observed hierarchical structures can be interpreted as regional fractures of Britain, observed in various forms, from natural boundaries, such as National Parks, to regional divisions based on social class and wealth such as the well-known North-South divide. At smaller scales, cities are generated through recursive percolations on each of the emerging regional clusters. We examine the evolution of the morphology of the system as a whole, by measuring the fractal dimension of the clusters at each distance threshold in the percolation. We observe that this reaches a maximum plateau at a specific distance. The clusters defined at this distance threshold are in excellent correspondence with the boundaries of cities recovered from satellite images, and from previous methods using population density.