After decades of urban evolution, the world's major subway systems appear to be converging on an ideal form.
On the surface, these core-and-branch systems — evident in New York City, Tokyo, London or most any large metropolitan subway — may seem intuitively optimal. But in the absence of top-down central planning, their movement over decades toward a common mathematical space may hint at universal principles of human self-organization.
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.
This is a crucial point: If the subways followed a predetermined path, their evolution would only reflect a set plan. Instead, the convergence “is a sign that there are some basic, profound mechanisms that drive the development of urban systems,” said Barthelemy.