Distance-based iterated function systems on surfaces

Iterated Function Systems (IFSs) are a classical tool for proceduralfractal generation, but their formulation is strongly bind to theunderlying coordinate system, and thus limited to flat Euclideandomains. We introduce an alternative formulation for an entirefamily of IFSs, exclusively based on the notion of distances andgeodesic paths, that allows defining systems directly on Riemanniandomains, enabling the procedural generation of fractal patterns thatare aware of the underlying geometry.