Macro and Micro Dynamics of the City Size Distribution

Abstract

Complex systems evolve and grow from the bottom up. Their key characteristic is emergence in that the actions of the system's basic elements are uncoordinated yet their effects at greater scales appear organized. Hence we say that a complex system exhibits order at higher scales which is usually measurable using some scale-free characteristics. In city systems for example, it is clear that there is a hierarchy of sizes and that these sizes follow a scaling law which can be approximated by a power law. Within cities, different types of centre also follow such scaling not only in terms of their sizes but also in terms of their frequency and spacing. Such systems are sometimes said to exhibit self-similarity which means that if the system is examined at different scales, it appears the same; that is if a system has a certain pattern at one scale, this pattern can be transformed to another scale by enlargement or contraction so that it is impossible to see the difference between the two scales. Self-similarity is a key feature of geometries that are said to be fractal and in terms of cities, such fractal patterns have been widely observed (Axtell 2001). In this chapter we will exploit this fact by examining the pattern of city sizes which have a characteristic signature which is a power law. This signature which is sometimes referred to as the rank size rule is one of the most fundamental features of complexity in that many systems in the physical, natural and social world exhibit such scaling.