Cellular automata (CA) are discrete models that are being ever more widely used to study urban forms and, more broadly, to understand, simulate, and forecast land use changes (LUC). But LUC models are not based on CA dynamics alone and so they are not fully consistent with mathematical definitions of CA. Accordingly, to study urbanization, authors often use “constraint CA” or “geographic CA” (GCA), i.e., CA which are coupled with other models in order to integrate geographical assumptions related to urban form and to provide more realistic results. These complementary models are usually calibrated according to expert knowledge and do not lead to reproducible deterministic results. Consequently, there is often a sizeable gap between the theory of CA as defined in mathematics and their practical use for LUC. In this chapter, cellular automata are constrained by a Markovian process helping to determine the number of cells that can change from one land use category to another. Second, a potential model is used to create a suitability map and define the probability of a cell changing from one category to another. Finally, all these additional constraints lead to a suite of models which is clearly more complex than classical CA as it can be considered mathematically. Nevertheless, as far as possible, it presents GCA as a mathematical adaptation of CA integrating the geographical assumptions necessary for studying urban forms in a realistic way.
Antoni, J. P., Vuidel, G., Omrani, H., & Klein, O. (2019). Geographic cellular automata for realistic urban form simulations: How far should the constraint be contained? In Modeling and Simulation in Science, Engineering and Technology (pp. 147–162). Springer Basel. https://doi.org/10.1007/978-3-030-12381-9_7