The chaos in the crowd is only apparent, VIDEO math says it

The apparently chaotic movement of a crowd actually follows precise rules: in fact, to avoid clashes, people unconsciously tend to organize themselves into linear or curved lanes that can be predicted based on the shape of the space to be crossed. This is demonstrated by a mathematical analysis conducted by the University of Bath, in the United Kingdom. The results, published in Science, could be useful for studying the behavior of molecules, bacteria and animals.

Lane formation from University of Bath on Vimeo.

To investigate crowd behavior, the researchers asked a group of volunteers to move around an experimental arena that simulated different scenarios, including King’s Cross station in London. Analyzing the footage of their movements, real mathematical patterns have emerged.

“At first glance, a crowd of pedestrians trying to pass through two doors might look messy, but when you look closer, you see the hidden structure,” explains Tim Rogers. “Depending on the layout of the space, both classic straight lanes as well as more complex curved trajectories such as ellipses, parabolas and hyperbolas”.

The formation of these ‘lanes’ “does not require conscious thought: the participants in the experiment were unaware that they arranged themselves in well-defined mathematical curves”, Karol Bacik points out. “Order emerges spontaneously when two groups with different goals cross paths in a crowded space and try to avoid colliding. The cumulative effect of many individual decisions unintentionally results in the formation of lanes.”

The researchers also looked at what happens when pedestrians are given an indication from the outside, such as to overtake other people on the right. Adding this rule ended up changing the shape of the lanes causing them to curve and cause inevitable slowdowns.