Möbius IFSPick three ways to bend the plane — each one a Möbius map that always sends circles to circles — then hop a single dot between them at random. The landings pile up on a lacy fractal wrapped over the surface of a sphere. Drag to orbit, scroll to zoom.Barnsley's 1980s “chaos game” grew ferns from shrink-and-rotate maps. Swap those for Möbius transformations, (az+b) / (cz+d) on the complex plane, and the attractor becomes the limit set of a Kleinian group — the hand-drawn gaskets of Klein and Fricke in the 1890s, revived in Indra's Pearls. Stereographic projection then wraps the plane and its point at infinity onto the Riemann sphere, the natural home of these maps.