Art by Alondra Moreno Santana
People gather en masse for many reasons—sports games, musical festivals, religious services, and protests comprise just a few examples. But in all cases, there is something exhilarating about being part of the crowd. Especially in the wake of pandemic-era lockdowns and the rise of virtual interaction via social media, coming together in person can be a liberating or even transcendent experience. It is an opportunity to lose yourself in the larger collective, to be a part of something much greater than any individual on their own. Crowds are powerful.
But anyone who has ever been in a crowd knows how hazardous they can be. In especially dense crowds, the sheer mass of people presents immense dangers. Under enough pressure from the bodies of the people surrounding them, a person can be asphyxiated or have their bones broken while still standing up. And if you drop your glasses, don’t even think about bending down to pick them up—you could very easily find yourself trapped, trampled, or worse. Add in unpredictable motion and widespread panic, and large gatherings can turn into mass casualty events, called “crowd crushes,” in the blink of an eye.
In recent years, it seems that crowd crushes have become even more common. In November 2021, a crowd crush at Travis Scott’s Astroworld music festival killed ten concert-goers and left twenty-five others grievously injured. In October 2022, a crush at a Halloween festival in Seoul killed 159 people and injured 197, marking the deadliest disaster in South Korea in almost a decade. And most recently, in January 2025, a series of deadly crushes at the Kumbh Mela pilgrimage festival killed dozens and injured perhaps hundreds more.
On the ground, these were terrifying scenes of pure chaos. But to François Gu, who recently earned his PhD in physics at the French university Ecole Normale Supérieure (ENS) de Lyon, these crowds are anything but chaotic. As he was beginning his studies, his mentor Denis Bartolo showed him a video of a massive, dense crowd in Pamplona, Spain. The crowd was gathered for the Chupinazo, the kickoff of the Festival of San Fermín, a massive, raucous celebration which features the famous “running of the bulls.” Rather than perceiving chaos, Gu saw the seeds of order. “I was pretty amazed by what we could see. It’s the kind of video that has a ‘wow’ effect—to see that many people crammed together, shoulder to shoulder, torso to torso, and to see everyone moving simultaneously. I really wanted to understand what was going on,” Gu said.
After years of researching the physical properties of large gatherings, Gu, Bartolo and their collaborators published a paper in Nature entitled “Emergence of collective oscillations in massive human crowds.” Their results were shocking—the team found that once a crowd hits a certain density threshold, it begins to exhibit patterns of oscillation, organizing into waves of density which churn around in massive vortices. This large-scale collective behavior offers key insights into the nature of crowd dynamics, and may lead to future breakthroughs in crowd monitoring and crush prevention.
The source of their findings was an ingenious piece of intuition: that large, dense crowds behave like a continuous fluid-like material, rather than an ensemble of individual particles. Treating the crowd as a fluid meant that the team only had to keep track of a few key variables—the density and velocity at every point over time. This treatment also helped the team simplify the problem, eliminating potentially erroneous assumptions about the physics of interactions between individuals. “By treating crowds as continuous media, we didn’t have to assume anything about the interaction rules between the pedestrians. We could just measure some macroscopic properties of the crowd,” Gu said.
In order to measure these density and velocity fields, Gu and the team employed a sophisticated machine learning tool to track how individuals move throughout a crowd. The team tested their algorithm on video data from the Chupinazo, which provided several benefits. First, the crowd at the Chupinazo assembles each year in the exact same place, allowing the team to control for extra potential variables. Second, the Chupinazo crowd always grows slowly over the course of an hour, meaning that the team could pinpoint the relationship between crowd density and any emergent effects.
The team analyzed the data using a Fourier transform, a mathematical tool which can tell us how different frequencies comprise a convoluted signal. Just like how a chord on a piano might be decomposed into many musical notes, a complex field of motion can be decomposed into many oscillations at different speeds. Applying the Fourier transform to their velocity field data, the team found something surprising. Below a density threshold of four people per square meter, the crowd moved loosely and chaotically, as expected. In the Fourier transform, this motion manifested as “zero-frequency oscillation,” jerky and unpredictable movement with no obvious patterns. However, above this threshold, the Fourier transform suddenly jumps to life, bursting with activity along an entire spectrum of oscillatory frequencies—now, the crowd moves in enormous vortices. “This transition from zero-frequency oscillations to oscillations with a finite frequency—this is when the threshold of four people per square meter is hit,” Gu said.
But what actually causes these oscillations? The team found they could model the system of people pushing against each other as one gigantic mass, held in place by an array of springs. If the mass moves too far away from the center, the springs push it back into place, providing a restorative force. However, the mass can move around the center with minimal resistance, allowing it to move in broad circular orbits.
Going forward, the team believes that understanding these collective oscillations will be key to preventing future crowd crush disasters. As evidence, they point to data from the Love Parade disaster in 2010, a now-infamous crowd crush in Germany which killed twenty-one people. Analyzing the data, the team found that the same oscillations they observed in the Chupinazo were present at the Love Parade. “To get a grasp of what kind of oscillations we’re talking about —it’s five hundred people, several dozens of tons all moving in the same direction. Now imagine you are standing next to a wall, and you have that amount of people coming at you,” Gu said.
However, what makes these oscillations so useful is that they appear long before crowd crush conditions emerge. “The key result is that we can detect the onset of these oscillations while they’re still very small—too small to be seen on a video. We know that if these oscillations appear, and the crowd continues getting denser, it’s probable these oscillations will grow at higher densities,” Gu said. This fact means that in the future, authorities might be able to use camera data to predict crowd crush behavior long in advance, allowing them time to implement measures which could save lives. “By just measuring the velocity field, and analyzing its spectral properties, you can detect the onset of the oscillations, and maybe you can prevent an accident […] up to twenty minutes in advance,” Gu said.
Going forward, Gu hopes to keep using physics on a tangible scale, applying his skills towards real-world problems. Having recently graduated from ENS de Lyon, he is now moving to the US, where he’ll continue working on problems related to physics and urban life at MIT. “At MIT, I’ll be joining the Senseable City Lab. I’m going to switch a bit, and work in urban science. I’m excited to apply my physics expertise to make cities more resilient and sustainable,” Gu said.