An adolescent’s bedroom notwithstanding, order can develop out of chaos. Take the universe, for example: it began in violent disarray, but over time has resolved itself into stars, galaxies, clusters and other structures.p. Or take a concert hall at the end of a great performance. While not quite cosmic in scale, something of a big bang occurs there as well — wild clapping by an appreciative audience. In the United States, this applause usually remains random and disorderly until it dies out. But in some cultures, particularly in Eastern Europe, it is common for an audience’s clapping to become synchronized into waves of rhythmic applause.p. Now, researchers in the United States, Romania and Hungary think they understand why order can arise spontaneously in a cheering crowd. The phenomenon of rhythmic clapping, the scientists reported last month in the journal Nature, follows a mathematical model for what are known as coupled oscillators. But it also has cultural roots.p. The researchers, Dr. Albert-Laszlo Barabasi, an associate professor of physics at the University of Notre Dame, and colleagues, studied “oscillators” — in this case, people clapping — in concert halls in Romania and Hungary and in a laboratory. Dr. Barabasi said that they discovered that clapping has two modes: fast, as occurs immediately at the end of a performance, and slow, as people cut the rate, or frequency, of their claps roughly in half.p. Within the two modes, of course, individuals clap at slightly different rates. But the range of rates is markedly different between the two modes. When people clap fast, Dr. Barabasi said, there is a wide range of rates; when they slow down, the variability all but disappears.p. The researchers applied this change in variability to a mathematical model for synchronization developed by a Japanese physicist, Yoshiki Kuramoto. Using this model, they discovered that when the range of rates is wide, as during fast clapping, synchronization is impossible. “But when the audience slows down, it meets the mathematical conditions for synchronization,” Dr. Barabasi said. In fact, he noted, under such conditions synchronization becomes inevitable, and the audience appears to clap as one.p. This is perhaps one of the more unusual examples of synchronization in nature but it is by no means unique, said Dr. Steven Strogatz, a professor of applied mathematics at Cornell, who is familiar with the work of Dr. Barabasi’s team. Among other examples, Dr. Strogatz said, is the synchronization of thousands of pacemaker cells in the heart, each of which produces an electrical discharge. And women who live together, he noted, often find that their menstrual cycles become synchronized over time.p. “It’s been recognized for 40 to 50 years that there’s a mathematical unity to these phenomena,” Dr. Strogatz said. “It’s a beautiful part of mathematics.”p. “It’s nice to see this phenomenon documented,” he added, referring to Dr. Barabasi’s work.p. Synchronization is not limited to humans, or even to living things. In parts of Southeast Asia, male fireflies sitting in the same mangrove tree will synchronize their flashes, creating a pulsing beacon that can be seen for miles. And synchronization was first observed not among creatures but among clocks. Christiaan Huygens, the 17th century Dutch mathematician and astronomer, noted that pendulum clocks on the same wall would eventually become synchronized. Vibrations carried in the wall did the trick.p. Unlike clocks or fireflies, rhythmic applause appears to have a basis in culture as well as physics, Dr. Barabasi said. The reason it occurs so frequently in Eastern Europe is that concertgoers know how to play the “game” of slowing down to achieve synchronization. “It doesn’t happen in America because people don’t slow down,” Dr. Barabasi said. “They are not aware of the game.”p. Even in an Eastern European audience, however, the rhythmic applause usually lasts only 10 or 15 seconds. It breaks down as synchronization is lost, often to be regained again, and can cycle this way over and over.p. The rhythm breaks down, the researchers theorized, because although synchronized clapping is distinctive, it is not particularly noisy — there are fewer claps in a given time period because the audience has slowed down. So enthusiastic members of the audience start to clap faster to raise the noise level, increasing the variability in clapping rates and destroying the conditions for synchronization.p. The only way rhythmic clapping could continue unabated, Dr. Barabasi said, would be if the audience was polite but unenthusiastic — if it was satisfied with the relative quiet of synchronized applause. Dr. Barabasi, who was born and raised in Romania and left for the United States in 1991, suggested that this was precisely what happened during speeches by totalitarian Eastern European leaders. They were met with prolonged, rhythmic applause, but seldom with enough enthusiasm to create chaos.