Urban morphogenesis: Putting mathematics in its place

Abstract

Mathematics is essential in a formal treatment of urban morphology because the complexity of urban form is best represented as a mathematical object, a fractal. Mathematics is equally important in models of morphogenesis. Nevertheless, mathematics in itself is incapable of representing morphogenetic processes and must be embedded in algorithms in order to capture the temporality of morphogenesis. In the case of straightforward processes of urban self-organisation, conventional simulation models are sufficient. However to capture the creativity of cities—their ability to create new agents and new types of agents with new rules of behaviour—unconventional algorithms are required, algorithms that alter themselves during execution. Ultimately algorithms, not mathematics, provide the natural language of morphogenesis.