From patterns to planning: modern mathematical models for the design of adaptive cities

Since the late 1970s, urban modelling has increasingly relied on mathematical tools, such as cellular automata, multi-agent systems, and fractal geometry, to better understand and predict – as far as possible – the evolution of cities. These methods allow researchers and urban planners to simplify the complex and dynamic nature of cities into manageable models, which can be used to simulate the evolution of some features, such as street networks, urban sprawl, and infrastructural changes. Moreover, the use of data analysis and artificial intelligence (AI) is leading to an evolution of these mathematical models, allowing for more adaptive simulations and for the creation of a range of future scenarios. The role of mathematical models in urban design is here analysed through a spectrum of historical examples, from morphogenetic models and cellular automata to AI for the study of adaptive and sustainable solutions. This bibliographic research is also the basis of an exhibition at the library of the IUAV University of Venice, where this historical background interacts with the studies of an international network of experts and ongoing research at IUAV.