Winding: 1/2
Mode Locked
θ_{n+1} = θ_n + Ω + K/2π·sin(2πθ_n)
Arnold tongues are regions of parameter space where the winding number is rational (mode-locked). Between them: quasiperiodic orbits.
At K=1 (dashed), tongues touch and overlap — the transition to chaos. The devil's staircase maps K → W(Ω) at fixed K.
Top: Arnold tongue diagram (K vs Ω). Red dot = current params.
Bottom: Orbit trajectory θ_n mod 1 over time.