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Torus Flow

Geodesics and flows on a torus. When the ratio p/q of two frequencies is irrational, the orbit never closes — it densely covers the entire surface (ergodic flow). Drag to rotate.

p (toroidal ω) 3.0
q (poloidal ω) 7.0
R (major) 2.0
r (minor) 0.60
Trail length 2000
Torus knot T(p,q): winds 3 times toroidally, 7 times poloidally. Closed if p/q rational — a knot! Irrational → dense orbit.