This gallery contains some animations I created in 2005 showing ray-traced convex hulls of limit sets of families of Kleinian groups. They were created with the open-source program

POV-Ray.

I'm certainly not the first person to make pictures of limit sets and their 3-dimensional convex hulls using ray-tracing; for other similar galleries of this type, see:

### Rendering details

#### Software and Hardware

The animations were rendered with POV-Ray 3.5 on a linux machine with dual AMD Opteron 250 processors and 2Gb of RAM. Per-frame render times ranged from several minutes to about one hour. The POV-Ray scene files were simple wrappers for the output from

lim2pov to set up the lighting, backgrounds, materials, etc.

#### Backgrounds

Some of the limit sets are rendered with pages from the mathematical writings of Fricke, Klein, Poincaré, etc., in the background. These scanned pages were taken from the archive of

historical mathematical monographs at Cornell.