[Hopf Fiberation of 3-sphere](http://mathematica.lossofgenerality.com/2012/08/31/hopf-fibration/)
It might take a few seconds to load, the controls are primitive but you get the idea
The code is there for you to review, one could easily change the parametrization. One could add translucent torus...
You could Export a movie or you could ray trace an animation, or you could export the geometries in polygon form and have another package render or ray trace.