Tori swept out by Hopf fibers over circles of latitude on $S^2$, nested and stereographically projected
This program visualizes tori that arise naturally from the Hopf fibration of S^3. Each circle of latitude on the base 2-sphere corresponds to a torus in S^3 swept out by the Hopf fibers over that circle. These tori are nested inside each other and, when stereographically projected to R^3, produce the familiar Hopf tori: a family of tori filling all of 3-space, each one the surface of revolution of a Villarceau circle. The program renders several of these tori to show how they nest.
Controls: Click and drag to orbit, scroll to zoom.
