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Urbanization is one of the defining trends of our time and appropriate models are needed to anticipate the changes in cities, which are largely determined by human behavior. In the social sciences, where the task of describing human behavior falls, a distinction is made between quantitative and qualitative approaches, each of which has its own advantages and disadvantages. While the latter often provide descriptions of exemplary processes in order to describe phenomena as holistically as possible, the goal of mathematically motivated modeling is primarily to make a problem tangible. Both approaches are discussed in terms of the temporal evolution of one of the dominant settlement types in the world today: informal settlements. These areas have been modeled in conceptual works as self-organizing entities and in mathematical works as Turing systems. It is shown that the social issues surrounding these areas need to be understood both qualitatively and quantitatively. Inspired by the philosopher C. S. Peirce, a framework is proposed in which the various modeling approaches describing these settlements can be combined to arrive at a more holistic understanding of this phenomenon by using the language of mathematical modeling.