Limit
The images below picture limit sets of Kleinian groups generated by two Moebius transformations. They were generated with C code written by Chris King, with some Python overlay to ease the image generation and quality. Chris King's code is itself based on the book Indra's Pearls, by David Mumford, Caroline Series and David Wright.
For suitably chosen Moebius transformations, the limit set is an Apolonian gasket, shown below.
But an incredible diversity of other fractal shape can arise.
