Möbius Strip & Klein Bottle

Möbius / Klein — parametric models of non-orientable surfaces. On the Möbius strip, the yellow seam identifies (u=0,v) with (u=2π,−v). Enable the ant and let it complete one round: its marked side reverses; only after two rounds is it original again. The Klein bottle is shown as an immersion in ordinary three-dimensional space. Its visible self-intersection is a drawing-space crossing, not a seam or a physical passage through the surface; its topological gluing is encoded by the parameter mesh.