A ruled surface that holds the Möbius twist inside a changing geometry. Click the top and the strip tapers to a cone — possibility narrowing to a point. Click the bottom and it opens into an inverted funnel — expansion from a singular source. Click the middle and it breathes as a cylinder — the strip's width constant, the loop infinite. Click the edge and the waist pulls in: a hyperboloid, the geometry of cooling towers and spacetime near a black hole.
The spiral staircase. Each latitude ring is a circle at a different radius. The Möbius twist means the top of the ribbon connects to the bottom after one full revolution — so what looks like a descending staircase is actually one continuous surface. You never leave the strip. You only think you're going somewhere new.
The click geometry. Your click position maps to two parameters: vertical position sets the taper ratio (top-heavy = cone, bottom-heavy = inverted cone), horizontal offset from center sets the waist depth (center = cylinder, edge = hyperboloid). These are real geometric families — cones, cylinders, hyperboloids are all ruled surfaces, all deformations of the same topological object.
The vortex feeling. The particles flow along the surface in the direction the geometry suggests — downward into a cone, upward from an inverted cone, spiraling in a cylinder. The flow never reaches a destination. It is always in motion on the same single surface, the same single edge.