A falling leaf is a genuinely studied chaotic aerodynamics problem: unlike a compact stone, a flat leaf's own tilt strongly changes the aerodynamic force it feels. When the leaf tips even slightly off broadside, the air pushes asymmetrically — generating both drag and sideways lift — and that lift creates a torque that tips the leaf further. The tilt keeps changing the force, which keeps changing the tilt: a real feedback loop between rotation and aerodynamics, the same coupling studied in falling-card and falling-leaf dynamics research.
Which pattern wins — flutter (bounded side-to-side rocking), tumble (sustained end-over-end spin) or a stable glide — depends on the leaf's dimensionless inertia-to-drag ratio I* (shown live), set mainly by size and mass: light, broad leaves are easily spun up by aerodynamic torque and tend to flutter or tumble, while the same shape held flatter and denser resists it. Curvature acts on a separate axis — a cupped or curled leaf behaves like a tiny parachute cup with a strong self-righting "weathervane" torque, damping out rotation and settling into a steady diagonal glide almost regardless of I*, which is why curled dead leaves tend to spiral down calmly while flat fresh ones flutter erratically.
The fading trail traces the leaf's actual path — watch it turn from a jagged zigzag (flutter/tumble) into a clean diagonal line (glide) as you raise the shape slider, and drag the wind slider to see how much longer a fluttering leaf spends exposed to horizontal wind than a leaf that glides straight down.