Thompson groups are an interesting mathematical object.
Their generalization to n dimensions are also interesting, but not easy to deal with. This project provides a platform to play with the elements of the group - in particular, to visualize them (in dimension 1 and 2), do basic computations, and explore questions such as conjugacy and growth.
Algorithms and math background: see the poster about this project [PDF].
For a general introduction to Thompson groups, see CFP. The program uses a notation compatible with the examples of that paper.