The movements of a crowd are not chaotic but predictable
Crowds can be intimidating or even terrifying to some people. Their movements can lead to tragic incidents. That is why it is essential to understand them better. A new study shows that these movements are not chaotic, as one might imagine, but rather nearly circular and periodic.
François Gu, Massachusetts Institute of Technology (MIT) and Benjamin Guiselin, University of Montpellier
Have you ever found yourself in the middle of a dense crowd in a confined space: on crowded subway platforms during rush hour, outside a bookstore for the release of a best-selling author’s latest book, or in front of the stage at a concert? Beyond the discomfort caused by frequent, involuntary physical contact with those around you, these situations seem uncontrollable and potentially dangerous: you feel compelled to move in a way dictated by impatience or the pressure exerted by others. But what is the true nature of individuals’ movements within a dense crowd? And can we understand its origins, particularly in order to prevent tragedies?
If we go by our intuition, these movements seem random and unpredictable. However, our study—conducted by the team of Denis Bartolo, a professor at ENS Lyon, and recently published in the journal *Nature*—reveals a counterintuitive phenomenon: instead of disorderly chaos, the crowd moves collectively in a regular and spontaneous pattern. Beyond a critical density of four people per square meter (imagine four people in a shower stall!), and without any external instructions, the crowd spontaneously adopts a nearly circular and periodic movement.
Our experience: the Pamplona Festival and its "Chupinazo"
Our first challenge in characterizing the dynamics of dense crowds was a daunting one: conducting experiments to film, from a good vantage point, the movements of hundreds of people, while preventing accidents. It was therefore clear that we couldn’t do this in our laboratory. The perfect opportunity arose when Iker Zuriguel, a professor at the University of Navarra, told us about the San Fermín festival in Spain. Every year on July 6, around 5,000 people gather in Plaza Consistorial in Pamplona for the “Chupinazo” ceremony, which marks the start of a week of festivities. The density reaches about 6 people per square meter!
This square, which measures 50 meters long by 20 meters wide, is surrounded by multi-story buildings whose balconies offer a breathtaking view of the activity taking place in the square. Over the course of four events, we used eight cameras positioned on two balconies to film the crowd’s movements in very high resolution. We have thus collected a dataset that is unique in the world for the study of dense crowds.
The crowd sways in unison
Using a technique employed, for example, in aerodynamics, we were able to map the movement speeds within the crowd, much like tracking air currents around an airplane. We found that everyone within a radius of about 10 meters was moving in the same direction.
During the “Chupinazo,” the crowd density is extremely high, at around six people per square meter: imagine, then, about 500 people moving together spontaneously, which amounts to a mass of several dozen tons in motion.
We also showed that the direction of this crowd’s movement gradually shifted before returning to its starting point every 18 seconds. In other words, individuals do not move chaotically, but follow nearly circular and periodic paths.
This slow movement can be explained by the fact that it is not individual people moving, but several hundred people moving in unison.
Finally, we observed that the crowd’s oscillating circular movements occur both clockwise and counterclockwise, even though the majority of people are right-handed ortend to pass each other on the right in Western countries. Cognitive and biological factors are therefore no longer relevant for explaining the movement of large groups of people in dense crowds that are swept up in very large-scale movements.
The Origin of Spontaneous Oscillations in Crowds
To mathematically model the dynamics of a crowd—consisting of a group of pedestrians—it seems natural to treat individuals as interacting particles.
Consider a pedestrian in this crowd. They are subject to forces that set them in motion. These forces may have a physical origin—such as contact with a wall or another pedestrian—or a cognitive origin—such as when trying to avoid another pedestrian. Unfortunately, the mathematical modeling of these forces relies on numerous unverifiable assumptions about individual behavior, making this approach unworkable.
In reality, it is not necessary to describe the dynamics of each individual to predict the dynamics of the crowd. Consider the flow of water through a pipe: the laws of physics allow us to predict the flow of water, even though it is impossible to determine the force acting on a single water molecule within that flow.
We therefore derived the equation describing the motion of a group of individuals moving together, without specifying the laws governing the motion of a single pedestrian. Our approach uses only fundamental principles of physics (conservation of mass, conservation of momentum) and makes no behavioral assumptions about the movement of individuals. It allowed us to construct a mathematical model whose solution showed excellent agreement with experimental observations.
A new method for preventing crowd accidents?
We also analyzed footage from surveillance cameras at the 2010 Love Parade in Duisburg, Germany. Although this crowd was very different from the one at the “Chupinazo,” we observed the same collective oscillations. This suggests that this mass behavior is universal, regardless of the type of event or the profile of the participants.
As we noted earlier, these oscillations can set dozens of tons in motion. We believe that such an uncontrolled movement of mass can become dangerous. During the “Chupinazo,” no accidents have ever been reported, likely because the event is short (one to two hours) and participants attend of their own free will, with some awareness of the risks. This was not the case at the 2010 Love Parade, where an accident caused dozens of deaths and hundreds of injuries. Just before the accident occurred, we detected these oscillations.
This detection can be performed in real time through a direct and straightforward analysis of surveillance camera footage. And since this dynamic is universal, the same method could be applied to other crowds. Thus, our findings could, in the future, inspire the development of tools for detecting and preventing mass accidents.
François Gu, Postdoctoral Researcher, Massachusetts Institute of Technology (MIT) and Benjamin Guiselin, Assistant Professor of Physics, University of Montpellier
This article is republished from The Conversation under a Creative Commons license. Readthe original article.