OPTi is a research tool in the field of Kleinian groups. OPTi visualizes quasi-conformal deformations of the once punctured torus groups by interactively drawing the isometric circles, the Ford region, the limit set, etc.
If this explanation does not make sense to you, you can still enjoy OPTi. Just drag the red and blue dots and see what happens.
Re-implemented the demonstrations of cone manifold deformation. Enable the menu in Preferences.
Opti by Masaaki Wada
Of course to use this program you have to have some idea what you are doing. But if you do, if you have some acquaintance with Kleinian groups, their fundamental domains and their limit sets, this program is imply awsome. I clearly illustrates all kinds of phenomena that are almost impossible to understand without, like geometric limits of Kleinian groups.
Wada has done a phenomenal job, and the mathematical community that this concerns can only be eternally grateful. John Hubbard, Cornell, University
As always, OPTi allows us to see amazing limit sets of Kleinian groups. Thank you so much for bringing OPTi up-to-date for new hardware/OS.