Fractal limit sets and Schottky groups

Goal:

The Möbius maps are transformations of the plane sending circles and straight lines to circles and straight lines, and preserving the angles between curves. Schottky groups are some particular groups consisting of Möbius transformations, and constructed by pairing couples of circles. Whenever such a group is given, there is an associated subset of the plane, called its "limit set". These sets have lots of symmetries related to the Shottky group, and are very often beautiful fractal sets.

The goal of this project is to be able to draw and explore these beautiful subsets of the plane. It will be also a nice opportunity to understand Möbius transformations and their link with 2x2 matrices, as well as some topics around groups.

Supervisor: Miguel Acosta

Difficulty level: Any.

Tools:

Literature:

FSCT -- University of Luxembourg