Every July, at the opening ceremony of the San Fermín festival signaling the imminent start of the running of the bulls in Pamplona, Spain, more than 5,000 people cram into the city’s central plaza. The crowd starts the morning dressed in white. By noon, much of their clothing has been dyed pink by the free-flowing sangria.

Participants in the event have described the raucous crush of people to Denis Bartolo, a physicist at the École Normale Supérieure in Lyon, France, who hasn’t dared step foot in the plaza himself. “The density of people is so high that it’s not just that you’re feeling uncomfortable,” he said he’d been told. “It becomes painful, like you can feel pressure on your chest.”

Over several years, he filmed and studied the event with the goal of perhaps one day helping prevent stampedes that can turn lethal in large public events. In a paper published Wednesday in the journal Nature, Dr. Bartolo and his colleagues say it may be possible to predict the spontaneous motion of a large crowd in a confined space once the density of people crosses a critical threshold.

Studying large, densely packed crowds is notoriously difficult. “You cannot just invite a thousand people to participate in an experiment,” Dr. Bartolo said. Even if he could, “I wouldn’t know how to guarantee their safety,” he added.

That’s why the San Fermín festival was so appealing. It involves thousands of people who gather predictably, and relatively calmly, each year.

Dr. Bartolo and his colleagues mounted cameras on the upper balconies of two buildings on opposite sides of the plaza to film the attendees amassed below. “If you take a look at the video, indeed the dynamics seem to be erratic, chaotic, turbulent,” he said. But he wondered whether he could tease out an organizing principle that governed the movements of the crowd.