The letters in the demo above label the matrices representing a few different
groups mentioned in another demo I have here. The circle on the left represents
and the circle on the right is the image of under the selected matrix.
Some interesting things to notice are that the matrices representing the surface group heavily compress
and the matrices representing the triangle group are orientation reversing.
If you want to learn all the details behind this demo and its use in my work at the Texas Experimental Geometry Lab, read my groups detailed report
here!