  Quantifying the spatial organization of human settlements is fundamental to
understanding the complexity of urban systems. However, the quantitative
patterns of the distribution of villages, towns, and cities that lie between
random and regular, are still largely unknown. Here, by analyzing the
geographic location of settlements in diverse regions, we show that the
apparently complex urban systems can be characterized by disordered
hyperuniformity (with small density fluctuations), an intriguing pattern that
has been identified in many physical and biological systems, but has rarely
been documented in socio-economic systems. By introducing the mechanisms of
spatial matching and competition, we develop a growth model that shows how
settlements evolve towards hyperuniformity. Our model also predicts the
heavy-tail population distribution across settlements, in agreement with
empirical observations. These results provide insights into the
self-organization of cities, and reveal the universality of spatial
organization shared by social, physical, and biological systems.
