One-dimensional urban scaling

In this paper, we use recent findings from urban scaling theory to evaluate how it could be applied to a one-dimensional archetypal city. Our focus is on how the simplicity of a one-dimensional model can provide intuitive insights that might be obscured in more complex, multidimensional models. With this instructive model, it is possible to visualize that if the population’s accessibility decreases more slowly than the increase in distance, an agglomeration effect occurs. This leads to increasing returns to scale when considering interactions between people or economies of scale in the case of amenities that serve the city. These findings highlight a key characteristic of complex systems: interacting parts that together exhibit properties that do not occur when they are isolated. The results presented here are derived from both numerical simulations and theoretical analysis. Although one-dimensionality is used here as a simplification, many organically evolved cities (e.g., Sułoszowa in Poland) and master-planned developments (e.g., The Line in Saudi Arabia) worldwide are shaped this way.