Mathematical foundations of cellular automata and complexity theory

Abstract

This chapter covers the mathematical foundations of cellular automata (CA) and complexity theory as the basis for models of urban forms and processes. CA have been used for both urban growth models and for more general simulation of land use changes, especially those driven by urban expansion. The chapter covers the origins of CA in the work on von Neumann and others, of complexity and emergence, some theory of CA behavior, and of the general form of CA models of urban systems. Particularly, research has paid attention to the methods for calibration of urban models using real data and of using such data to extract the rules governing state changes in CA. CA models have been shown to be a good combination of being light in data demands, yet accurate and robust in modeling and forecasting.