  This study investigates city dynamics employing a nonextensive diffusion
equation suited for addressing diffusion within a fractal medium, where the
nonadditive parameter, $q$, plays a relevant role. The findings demonstrate the
efficacy of this approach in determining the relation between the fractal
dimension of the city, the allometric exponent and $q$, and elucidating the
stationary phase of urban evolution. The dynamic methodology facilitates the
correlation of the fractal dimension with both the entropic index and the urban
scaling exponent identified in data analyses. The results reveal that the
scaling behaviour observed in cities aligns with the fractal dimension measured
through independent methods. Moreover, the interpretation of these findings
underscores the intimate connection between the fractal dimension and social
interactions within the urban context. This research contributes to a deeper
comprehension of the intricate interplay between human behaviour, urban
dynamics, and the underlying fractal nature of cities.
