Fluid flow on a manifold

Read the field as fluid velocity. Each dot follows the integral curve through its initial position; the entire dot cloud is the “flow” Φ_t applied to every starting point at once. Try the presets: rigid rotation spins the cloud; the saddle stretches it along one diagonal and compresses along the other; the source and sink reveal divergence; the shear distorts the cloud without changing area. The Lecture-5 default field is a gentle non-uniform drift.