Arapaima Air-Breathing Lab: Kuramoto Surfacing Synchrony (2D)
2D companion: each arapaima's air-debt phase grows with dissolved-oxygen deficit and couples to its shoal-mates through a Kuramoto phase-oscillator model, so surfacing-to-breathe synchronizes above a critical coupling strength.
This 2D companion replaces the 3D lab's orbiting river scene with the actual mechanism behind arapaima surfacing behaviour: an unbounded air-debt phase per fish, driven by a dissolved-oxygen-deficit-scaled natural frequency and coupled to the rest of the shoal through a Kuramoto sine-coupling term, integrated with RK4. A phase-circle panel and a live synchrony trace make the Kuramoto phase transition — independent surfacing below critical coupling, locked-together surfacing above it — directly visible and directly verifiable against the order parameter, instead of only implied by a swimming animation.
2D Kuramoto phase-oscillator model of arapaima air-debt: each fish's surfacing phase grows with a hypoxia-scaled natural frequency and couples to its shoal-mates' phases, producing a real synchronization phase transition above a critical social-coupling strength.
2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install