Cities are understood as complex systems whose properties follow universal patterns governed by scaling laws. This approach proposes that various urban indicators—economic productivity, infrastructure length, energy consumption, innovation rates—scale predictably with population size. These relationships follow power laws: social quantities such as GDP or crime rates grow superlinearly (exponent >1), while infrastructural elements like road length grow sublinearly (exponent <1). This reveals that larger cities are not simply bigger—they are fundamentally more efficient and socially dense. This framework defines cities not by administrative boundaries but by spatial continuity of population density. A city is considered a coherent entity when it forms a connected cluster of high-density population. Through large-scale empirical data from multiple countries, it is shown that this method identifies consistent scaling exponents across different urban systems, suggesting deep structural regularities beneath cultural or historical differences. The model proposes that the underlying driver of these scaling laws is the intensification of social interactions with urban growth. As population increases, networks of exchange, innovation, and collaboration multiply, leading to accelerating returns. However, this also entails systemic vulnerabilities: congestion, inequality, and resource strain emerge from the same dynamics. This theory reframes urban growth not as a disorderly process, but as a mathematically predictable evolution, enabling more grounded urban planning, forecasting, and sustainability strategies.
Bettencourt, L. M. A. (2012). ‘The Origins of Scaling in Cities’. arXiv preprint arXiv:1207.4291.
