Squares that Look Round: Transforming Spherical Images
  We propose M\"obius transformations as the natural rotation and scaling tools for editing spherical images. As an application we produce spherical Droste images. We obtain other self-similar visual effects using rational functions, elliptic functions, and Schwarz-Christoffel maps. 
Saul Schleimer and Henry Segerman
cs.GR math.HO