Hidden order in chaotic crowds

Credit: University of Bath

Have you ever wondered how pedestrians “know” to cross lanes when moving through a crowd, without the matter being discussed or even consciously thought about?

A new theory developed by mathematicians at the University of Bath led by Professor Tim Rogers explains this phenomenon, and is able to predict when trajectories will be curved as well as straight. The theory can even describe the slope of a skewed trajectory when people have a habit of passing on one side instead of the other (for example, in a situation where they are frequently reminded to “pass on the right”).

This mathematical analysis reconciles conflicting views on the origins of orbit formation, and it reveals a new class of structures that may go unnoticed in everyday life. Found, reported in Sciencerepresents a major advance in the interdisciplinary science of ‘active matter’ – the study of group behavior in interacting populations ranging in scale from bacteria to herds of animals.

Tested in arenas

To test their theory, the researchers asked a group of volunteers to walk across an experimental arena that mimicked different layouts, with changes in entrance and exit ports.

One arena was set up in the style of King’s Cross Station in London. When the researchers watched the video footage from the experiment, they observed mathematical patterns that took shape in real life.

Professor Rogers said: “At a glance, a crowd of pedestrians trying to pass through two gates may seem disorderly, but when you look closer, you see the hidden structure. Depending on the design of the room, you can observe either the classical straight lanes or more complex curved patterns such as ellipses, parabolas and hyperbolas.”

Path formation

The single-lane processions formed at busy zebra crossings are just one example of lane formation, and this study is likely to have implications for a number of scientific disciplines, particularly in physics and biology. Similar structures can also be formed by inanimate molecules, such as charged particles or organelles in a cell.

Until now, scientists have offered several different explanations for why human crowds and other active systems naturally organize themselves into orbits, but none of these theories have been confirmed. The Bath team used a new analytical approach, inspired by Albert Einstein’s theory of Brownian motion, which makes testable predictions.

Encouraged by the way their theory matched the numerical simulations of colliding particles, they then teamed up with Professor Bogdan Bacik – an experimentalist from the Academy of Physical Education in Katowice, Poland – and ran a series of experiments (like the one modeled at King’s Cross) using human crowds.

Lead author Dr Karol Bacik said: “Lane formation does not require conscious thought – the participants in the experiment were not aware that they had arranged themselves in well-defined mathematical curves.”

“The order emerges spontaneously when two groups with different goals cross paths in a crowded room and try to avoid crashing into each other. The cumulative effect of many individual decisions inadvertently results in the formation of lanes.”

The researchers also tested the effect of externally imposed traffic rules – they instructed the participants to pass others on the right. Consistent with the theoretical prediction, adding this rule changed the trajectory structure.

“When pedestrians have a preference for right turns, the lanes end up tilting and this introduces frustration that slows people down,” Dr. Bacik said.

“What we have developed is a neat mathematical theory that predicts the propensity for lane formation in a given system,” Professor Rogers said. “We now know that much more structure exists than previously thought.”

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