City systems and complexity

We first present the systems approach as it developed in the physical and social sciences during the 20th century and how it provided a theoretical foundation for ill-defined systems such as cities. The notion of the system being constructed from the top-down manifesting a stable equilibrium which underpins the approach was found wanting and we sketch the way complexity theory developed in its wake. We introduce Weaverâ€sA„A´s threefold classification into simple systems, systems of disorganised complexity, and systems of organized complexity and suggest that these three types show different degrees of unpredictability in terms of the science underpinning them. We then outline the properties of city systems as they are revealed by complexity theory. We examine the size, scale and shape of cities in terms of how cities change qualitatively with respect to their size, introducing allometry, rank-size, and power laws which represent ways in which cities change as they grow and evolve through the hierarchy of size. We note central place theories and gravitational models and then illustrate how all these ideas can be tied together using concepts from information theory and entropy. We conclude with some reflections on the dynamics of complex systems, focusing on the need to use ideas from complexity theory to think about how the future form and function of cities might evolve.