The rapid increase of settlement structures demands the development of suitable models for their description. In this context, different approaches and works are known. An increasing amount of data leads to more and more complicated models. In this work an alternative approach is proposed, which uses the knowledge from the modeling of physical processes with the help of differential equations, in order to represent phenomena of the pattern formation in settlement systems. We propose a method to investigate the properties of settlement dynamics using the spatial and temporal changes in time resolved population density patterns. Starting from the more common finding in the literature that settlements often arrange themselves in a regular manner, we examine four fast-growing regions in the Global South using our methodology. Although no clear mechanisms could be identified in the approach presented so far, the workflow presented here creates the possibility of a new view on pattern formation processes to be studied geographically.