A paywalled paper in the Royal Society's journal Interface argues that the world's underground rail systems are all converging on an "ideal" form. The paper, "A long-time limit for world subway networks," shows that subway systems grow "organically," in response to the needs expressed by the cities above them over the course of decades, and reveal truths about the shape of cities. In Wired, Brandon Keim describes the findings:
Patterns emerged: The core-and-branch topology, of course, and patterns more fine-grained. Roughly half the stations in any subway will be found on its outer branches rather than the core. The distance from a city’s center to its farthest terminus station is twice the diameter of the subway system’s core. This happens again and again.
“Many other shapes could be expected, such as a regular lattice,” said Barthelemy. “What we find surprising is that all these different cities, on different continents, with different histories and geographical constraints, lead finally to the same structure.”
Subway systems seem to gravitate towards these ratios organically, through a combination of planning, expedience, circumstance and socioeconomic fluctuation, say the researchers.