Scaling Laws in City Growth: Setting Limitations with Self-Organizing Maps

Do scaling relations always provide the means to anticipate the relationships between the size of cities, costs of maintenance, and the socio-economic benefits resulting from their growth? Scaling laws are considered a universal principle that describes the development of complex systems such as cities. It seems that regardless of their location or history, the growth of cities is associated with the super-linear or sublinear scaling of features such as the amount of space required, infrastructure, or human activities. However, the results of our research, based on grouping by Self-Organizing Maps, reveal some limitations in the application of scaling laws: the trends of urban growth behave in a different manner when we consider both a large and diverse collection of cities and a subset of cities alike. This finding complements the existing body of knowledge on the growth of cities and allows for a more accurate prediction of their future.