The video shows a flow through the moduli of tori of revolution. The wrapping numbers in the sequence, suggested by Martin Kilian, are (1,3) → (2,3) → 2-wrapped → (2,5) → (3,5) → 3-wrapped → (3,4) → (1,4) → 1-wrapped.
The twizzled torus is a twist on the constant mean curvature surfaces of revolution in euclidean space, classified in 1841 by C. Delaunay. Each such surface has an associate family, which extends the rotationally symmetry to a screw motion. More recently, constant mean curvature surfaces in the three-sphere have been investigated, of which the equivariant tori are among the simplest examples.
The video shows a flow through the moduli of tori of revolution. The wrapping numbers in the sequence, suggested by Martin Kilian, are (1,3) → (2,3) → 2-wrapped → (2,5) → (3,5) → 3-wrapped → (3,4) → (1,4) → 1-wrapped.