#BézierCurve style interpolation¹ of #MöbiusTransformation going via 2x2 matrix diagonalization² as the linear interpolation base case.

Animation has 4 static transformations, the other 4 are interpolated along a loop between themselves.

Maybe a bit too fast and a bit too low resolution, fixing that is possible by applying more computing power. This version took 3m30s to render.

¹ https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm#Geometric_interpretation
² https://mathr.co.uk/blog/2015-02-06_interpolating_moebius_transformations.html