Cities are often purported to be scale-free. City sizes, for example, are apparently universally logarithmically distributed, and are thus exponentially more likely to be small than big. Such properties are referred to as “scale-free” because there is no “average” size or scale. In contrast, the interiors of urban spaces very generally have intrinsic scales and common structures. How scale-free behaviour can emerge through processes acting over intrinsically defined scales remains a generally open question.

The urban spaces project aims to understand the origins and properties of intrinsic scales in both one and two dimensions. One dimensional scales are examined in terms of distance decay functions, both in fundamental theoretical terms and through empirical analyses of several major world cities. Two dimensional scales are examined in terms of processes leading to the agglomeration or fragmentation of “neighbourhoods” delineated by spatial discontinuities.

In order to implement comparative analyses of some of the world’s largest cities, initial phases of this project have focussed on methodological development, including high-performance software. This software will be applied to a highly detailed, global-scale analysis of distance decay functions. Extending from a firm theoretical basis, this will provide a uniquely rich and detailed consideration of the origins, forms, and empirical properties of distance decay functions. The project’s second phase will furnish similarly detailed analyses of spatial discontinuities, extending from theoretical models for their origins, and ultimately providing a similarly detailed global-scale empirical analysis.