Scaling and allometry in the building geometries of Greater London

TL;DR

This paper investigates the scaling laws and allometric relationships of building geometries in Greater London, revealing strong scaling patterns and shape variations linked to building size and land use.

Contribution

It introduces a comprehensive analysis of intra-city building geometries using large-scale data, extending scaling laws to urban building structures and land use classifications.

Findings

Strong scaling in building heights and sizes in Greater London

Allometric relationships show how building shape varies with size

Correlation functions support non-spatial scaling analysis

Abstract

Many aggregate distributions of urban activities such as city sizes reveal scaling but hardly any work exists on the properties of spatial distributions within individual cities, notwithstanding considerable knowledge about their fractal structure. We redress this here by examining scaling relationships in a world city using data on the geometric properties of individual buildings. We first summarise how power laws can be used to approximate the size distributions of buildings, in analogy to city-size distributions which have been widely studied as rank-size and lognormal distributions following Zipf and Gibrat. We then extend this analysis to allometric relationships between buildings in terms of their different geometric size properties. We present some preliminary analysis of building heights from the Emporis database which suggests very strong scaling in world cities. The data base for Greater London is then introduced from which we extract 3.6 million buildings whose scaling properties we explore. We examine key allometric relationships between these different properties illustrating how building shape changes according to size, and we extend this analysis to the classification of buildings according to land use types. We conclude with an analysis of two-point correlation functions of building geometries which supports our non-spatial analysis of scaling.