Deformation of quasi-Fuchsian punctured torus groups
The following movie is a byproduct of my talk at Nakanoshima Osaka. The slides are available here. The parameter space of the upper right is the linear slice QF(2.0) in my slides.
For a theoretical background of this phenomenon, see Theorem 4.1 of Parker-Parkkonen's paper Coordinates for Quasi-Fuchsian Punctured Torus Space (Geometry & Topology Monographs 1, 451–478).