Limit Sets and Convex Hulls

Below are some limit sets of Kleinian groups and some of their convex hull boundaries. Click on the picture to see it enlarged.

View from inside the convex hull of the limit set of a
degenerate group (parameters by Curt McMullen).


Limit sets of quasi-Fuchsian groups arising from bending a
Fuchsian group. (The blue region is the domain of discontinuity.)

The algebraic limit of a partial-pseudo-Anosov
mapping class on Bers' slice.

The geometric limit.

The geometric limit on the
front of the sphere.

The Algebraic limit of iteration of the
(id,1145) mapping class on Bers' slice.

The Algebraic limit of iteration of the
(id,Inverse(1145)) mapping class on Bers' slice.

The geometric limit.

The geometric limit on the front of the sphere.

The algebraic limit of iteration of a
Dehn twist on Bers' slice.

The geometric limit of iteration
of a Dehn twist.
These pictures were generated by finding explicit generators for the appropriate Kleinian group (using Mathematica and computer programs of Curt McMullen) and using lim, a limit set generation program written by Curt McMullen .
Jeffrey F. Brock