Maths reveals key to stadium phenomenon.
How many fed-up fans does it take to start a Mexican wave? About 25, say researchers in Europe. Their computer models of crowds' behaviour could help control rowdy hooligans.
Since shooting to fame during the 1986 World Cup in Mexico, Mexican waves have surged through sports stadia worldwide. Spectators jump to their feet with arms outstretched - and sit down again as neighbours in the stand rise up.
Tamas Vicsek of the Eötvös University of Budapest in Hungary and his team studied footage of Mexican waves in football stadia and built a mathematical model that mimics them. Because people in the crowd are behaving in a predictable way, they fit similar equations to the waves of contraction that spread through the heart or fire razing a forest1.
It takes a critical mass of two- to three-dozen people to get the wave going, the researchers found. And waves will only spread during lulls in a football game or athletics event, predicts Vicsek, when viewers aren't otherwise distracted or overexcited.
Vicsek hopes that further studies will help predict when excited masses will run out of control, such as during riots or post-match brawls. "We could introduce policemen and simulate the effect of those," he says.
Farkas, I., Helbing, D. & Vicsek, T. Mexican waves in an excitable medium. Nature, 419, 131 - 132, (2002).