Stadium Waves

“Crescendo rising here. It’s amazing, I’ve never seen anything like this…”

-Sportscaster Joe Garagiola describing the first documented appearance of a "stadium wave" at the Oakland Alameda Coliseum on October 15, 1981.

Consider the stadium wave: a spontaneous group behavior in which people seated in sporting arenas rise and cheer in a pattern that resembles a traveling wave.

Beginning in the early 80's these human waves began appearing at sporting events all over the world. The phenomenon goes by several names, most commonly La Ola or the "Mexican Wave." Your typical stadium wave spans about 15 seats at any given moment and sweeps along at a brisk 20 seats per second (about 27 miles per hour). These waves will jump small gaps in U-shaped stadiums and reflect off dead ends. Over 60% of stadium waves travel clockwise.

It's easy to see how a wave keeps going once it has begun but how do you get one of these things started in the first place? There is no single individual who instigates a wave. Even several people working together may fail to set one off. Below we see a packed stadium and if you look closely you can see many people trying to start a wave to no avail.  

So when a wave does occur, how did everyone suddenly come into agreement that this is happening? What is the spark that starts this fire?

In order to answer this question let's begin by making some basic observations about how a stadium wave travels. Once it's going, the dynamics that drive it are fairly straightforward. Each individual in the stadium is essentially following this simple rule: copy your immediate neighbor. If your neighbor stands and cheers, you do the same. If they sit down you do the same, following course with some small delay. You can play with a simplified version of this dynamic below. Click on the seated person on the left and they will stand and cheer. The person on the right will mimic them after a slight delay and, by moving the blue slider, you can adjust the length of this delay.

Now imagine what happens when we line up several people in a row, each copying their neighbor in this way. Click on the leftmost person to start a wave and watch how it propagates down the line. How does adjusting the delay affect the wave's shape? Or the wave's speed? Can you get several waves going at once?

Obviously this is a gross oversimplification of how a stadium wave actually works. A more sophisticated stadium wave simulator was created by professor Tamás Vicsek of Eötvos Loránd University in Budapest. He began by watching videos of stadium waves, observing their characteristic size, form, velocity, and stability. He then began modifying certain computer programs that had originally been used to simulate how muscle pulses travel through heart tissue or how forest fires spread through a terrain. In the same way that we could adjust the delay in the above interactive to change the width and speed of our wave, Vicsek was able to tweak these programs to create simulated stadium waves that closely matched the complex behavior of real stadium waves.

Vicsek used his simulator to explore just how many people it takes to start a wave. What he discovered was a "sharply changing function" around the number 25. That is, no matter how excited the crowd is, it is unlikely that a wave can be instigated by less than 25 people. On the other hand, if the crowd is excited enough to support a stadium wave, it shouldn't take much more than 25 to get one started. 

Of course a real stadium wave does not begin with an organized confederacy of 25 people. Rather, these waves originate when a small handful of people begin performing a repeated mini-wave together and are gradually joined, one by one, by their neighbors. Eventually, when the size of this group reaches the mid-twenties, a miracle happens: the idea of "copying your neighbor" abruptly goes viral. The pulse escapes its creators and the entire stadium becomes consumed with the bizarre ritual of propagating this human wave.

From Busby Berkeley dance numbers to the North Korean Arirang Festival, it's clear that large groups of trained people can perform impressive feats of group coordination. What makes stadium waves fascinating to researchers like Vicsek is that they are a completely unchoreographed form of group action. “For a physicist," he explains, "the interesting specific feature of (the stadium wave) is that it represents perhaps the simplest spontaneous and reproducible behavior of a huge crowd with a surprisingly high degree of coherence and level of cooperation.”

Encounter more waves at After Dark: Catch a Wave this Thursday evening, January 5, at the Exploratorium.