Möbius Transformations on the Complex Plane and Riemann Sphere

Mappings by a Möbius (or bilinear) transformation are considered on both the complex plane and the Riemann sphere. A reference point and adjustable grid are specified in polar coordinates, and the mapping can be varied using eight real parameters specifying a Möbius transformation. Bookmarks can be used to save parameters illustrating some interesting properties of the transformation.