Why can slowing down help a crowd find a shared beat? Seats flash amber when they clap. Within about 120 ticks (4 simulated seconds) most of the hall flashes together.
Try this Once the crowd has locked, turn slow-clapping off (it takes effect live). The tempo doubles, the spread of preferred rates grows fivefold, and within 2 seconds synchrony falls to between about 0.05 and 0.3.
About this model Néda, Ravasz, Vicsek, Brechet and Barabási recorded theater and opera audiences (Nature, 2000) and found that synchronized applause comes with clapping at about half the usual rate, which narrows the spread of individual clapping frequencies. Steven Strogatz retells the finding in Sync (2003). This model reproduces the mechanism with Kuramoto-style phase oscillators.
The 96 audience members sit in 8 rows of 12. Each has a phase φ between 0 and 1 and a fixed pace offset drawn uniformly from −1 to 1. Each tick (1/30 s) every phase advances by rate/30, where rate = tempo + pace offset × spread + coupling × R·sin 2π(ψ − φ), and R and ψ are the length and angle of the audience's mean phase vector: the Kuramoto mean-field pull. A clap happens when a phase wraps past 1. With slow-clapping on, tempo is 1.65 claps per second and spread is diversity/5 (±0.16 at the default 0.8); off, tempo is 3.3 and spread is diversity (±0.8). All three controls are read every tick.
Everyone hears the whole hall equally (all-to-all coupling), and the mode is a switch you set: real audiences move between fast incoherent and slow synchronized clapping on their own, and this model has no mechanism for that. The tempos and spreads are illustrative, not fitted to the recordings. The slow crowd locks from a coupling of about 0.25; at 0.2 synchrony wanders between 0.4 and 0.7, and the fast crowd only partly synchronizes even at coupling 1.
