Continuum percolation and spatial point pattern in application to urban morphology

Abstract

One of the important problems in studying urban morphology is to be able to quantify urban objects using mathematical descriptions or measures. Doing so allows one to make a comparison amongst different types of geometry/morphology in urban systems, and effectively classify them. A number of techniques have indeed been developed in urban/geographical analysis. Here in this work, we propose a method to quantify spatial patterns of a set of points based on the idea of percolation, that is rooted in mathematical physics and has been applied to various fields. Employing the idea of percolation enables us to characterise the relative spatial arrangement of points in a set. In particular, the method could be applied to analyse the distribution of different point datasets in urban context and illustrate how it could characterise and classify their spatial patterns. We show that different spatial distributions of points can generally be classified into four groups with distinctive features: clustered, dispersed or regularly distributed at single or multiple length-scales. In applying to urban morphology, the results could enable quantitative discussion on the existence of two different forms of urban system: well-planned and organically grown.