Investigation of Clustering in Turing Patterns to Describe the Spatial Relations of Slums

Worldwide, about one in eight people live in a slum. Empirical studies based on satellite data have identified that the size distributions of this type of settlement are similar in different cities of the Global South. Based on this result, a model was developed that describes the formation of slums with a Turing mechanism, in which patterns are created by diffusion-driven instability and the inherent characteristic length of the system is independent of boundary conditions. It has not yet been taken into account that Turing patterns usually arrange themselves regularly, while slums are often found in clusters. Therefore, this study investigates to what extent a common reaction kinetics for Turing models can be adapted to represent a locally concentrated arrangement of objects and to adapt the size distribution of the objects to the empirical results. Based on a summary of the literature and two numerical studies, it can be shown that although it is possible to adapt the model to the empirical data, this also increases the complexity of the model.