title: Cities and regions in Britain through hierarchical percolation.
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.
authors.affiliation: Centre for Advanced Spatial Analysis (CASA), University College London , London, UK.
authors.forename: Elsa
authors.initials: E
authors.lastname: Arcaute
authors.affiliation: Centre for Advanced Spatial Analysis (CASA), University College London , London, UK.
authors.forename: Carlos
authors.initials: C
authors.lastname: Molinero
authors.affiliation: Centre for Advanced Spatial Analysis (CASA), University College London, London, UK; Center for Advanced Modeling, The Johns Hopkins University, Baltimore, MD, USA.
authors.forename: Erez
authors.initials: E
authors.lastname: Hatna
authors.affiliation: Centre for Advanced Spatial Analysis (CASA), University College London, London, UK; Consumer Research Data Centre, Geography, University College London, London, UK.
authors.forename: Roberto
authors.initials: R
authors.lastname: Murcio
authors.affiliation: Centre for Advanced Spatial Analysis (CASA), University College London, London, UK; Consumer Research Data Centre, Geography, University College London, London, UK.
authors.forename: Camilo
authors.initials: C
authors.lastname: Vargas-Ruiz
authors.affiliation: Centre for Advanced Spatial Analysis (CASA), University College London , London, UK.
authors.forename: A Paolo
authors.initials: AP
authors.lastname: Masucci
authors.affiliation: Centre for Advanced Spatial Analysis (CASA), University College London , London, UK.
authors.forename: Michael
authors.initials: M
authors.lastname: Batty
keywords: city boundaries; fractal dimension; percolation theory; street networks; urban hierarchies