Chapter 15: Thom’s catastrophe theory and Turing’s morphogenesis for urban growth modelling
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Among the new approaches that emerged in the field of complexity in the late 1950s, René Thom’s catastrophe theory and Alan Turing’s morphogenesis with reaction/diffusion equations are close cousins that have attracted the interest of geographers and social science researchers but have been soon replaced by multi-agent systems, probably because of the mathematical difficulties involved. However, both approaches have formal characteristics that make them very appropriate for modelling processes involving spatial differentiation and dynamics such as housing prices and population in an agglomeration. In this chapter, I review Thom and Turing’s legacy for geographers, present a new model of urban morphogenesis using these approaches and suggest new developments to further capture the complexity of urban systems in the models.

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