The World’s Road Networks, Visualized As Beautiful Flowing Fractals

“If cities are living things, roads are the veins that keep them alive, even at the mathematical level.”

Imagine you and a million other people were all at one point in a city, say the World Trade Center in New York, and everyone started traveling out in every possible direction all at once. One hour later, where would everyone be located?


That’s the question applied physicist Alberto Hernando de Castro, a researcher at Ecole Polytechnique Fédérale de Lausanne, asked as he generated beautiful animations that illustrate the patterns in road networks of 10 different countries. Each isochrone–places on the map with the same color at the same time–show all the points that can be arrived at simultaneously from the starting location.

Hernando de Castro, whose work involves creating mathematical models that describe urban behaviors, was looking to find the equations that describe “human diffusion,” as constrained by road infrastructure.

Isochrone map of U.S., with starting points at Golden Gate Bridge and World Trade Center

“If you see a person in a particular place, what is the probability of finding that person in any other place after one hour? Or two hours? Can we find a mathematical principle for that?” he says.

Turns out he could, and the structure described is a fractal, very similar to the way repeating structure can be found frequently in nature–such as in the roots of trees, the strikes of lightening, and the branching veins in our bodies.

“We checked and find the fractals everywhere, any country at any continent,” he says. If cities are living things, roads are the veins that keep them alive, even at the mathematical level.”

Hernando de Castro went on to create a predictive model that describes how transportation networks grow, prioritizing certain preferences like connecting cities that are close together and “optimizing resources.” You can see the results in the animations he presents.


Have something to say about this article? You can email us and let us know. If it’s interesting and thoughtful, we may publish your response.

About the author

Jessica Leber is a staff editor and writer for Fast Company's Co.Exist. Previously, she was a business reporter for MIT’s Technology Review and an environmental reporter at ClimateWire.