Latitudinal Tori

What we want to explore here is first how to measure the length of an orbit in a principal bundle, by applying cumulative G-actions, and then decimating it into a linear space in the form of an admissible curve with segments that measure in an equal way. Then, the result should be smooth looking Hopf fibers using only thirty cut points along the orbit. So, we defined a new function that takes a sequence of G-actions, which are spaced linearly and equally, and it spits out new G-actions that preserve the same symmetry under stereographic projection, which pushes forward a metric with non-constant curvature. As a result we rectified the distortion that was inevitable if we wanted to capture the Hopf fibration complete as a picture and in an efficient manner. Calculated the Möbius transformtions, at each frame of the animation, by taking four complex numbers that characterize the transformation, and rotating them in the Riemann sphere about the x² axis in E³. Made with and