MacKurt

Four hundred fireflies, each blinking at its own slightly different pace, start as random sparkle. Each one nudges its rhythm toward the flashes it sees. Below a critical coupling nothing happens; above it a crowd suddenly locks, and the whole field blinks as one. The switch is a phase transition, like water freezing. The model was written down by Yoshiki Kuramoto in 1975 for chemical oscillators. Real fireflies do it too: along some Southeast Asian rivers, thousands of males flash in unison, and early reports of it were doubted for years. The same maths describes pacemaker cells in the heart and the moment a concert hall's applause turns into clapping in time. In theory the switch sits at K = 1.0 (grey curve), and the crowd needs a little time to follow it.