Limit set pictures

In Oct. 1999 I prepared some slides for a general-audience talk (Tsukuba, Japan). In the process I looked for simple ways to make 3-dimensional renditions of convex-hull boundaries for Kleinian groups. I settled on POV-ray, a public-domain ray-tracing package, to which I fed lists of circles from Curt McMullen's lim. I also used David Wright's kleinian to search through the parameter space and produce some two-dimensional pictures.

The slides for the talk are Here.

Jeff Brock has made some nice animations using these programs.

See also the book Indra's Pearls by Mumford, Series and Wright, which is full of many really beautiful pictures, and gives a very good accessible introduction to Kleinian groups without the baggage.


Here are a few of the preliminary pictures I made, before I settled on a more pleasant color scheme...

The limit set of a Kleinian group near the boundary of Maskit's embedding of the Teichmuller space of a once-punctured torus (produced by McMullen's "lim" program), followed by two 3-D renditions of part of the convex hull boundary (produced by the ray-tracing program POV-ray):





The limit set of a quasi-Fuchsian punctured-torus group, followed by two 3-D renditions of part of the convex hull boundary (it looks more like a slug than I expected):




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