Three XI Seven

This is a graphical representation of a type of algebraic construct called a group. A group is basically the set of all of the transformations you can perform on a structure without permanently changing it. For example, if you've done image editing before, the set of flips & multiple-of-90 rotations you can apply to an image make up a group.

This specific group is the Semidirect Product of the cyclic group on seven elements with the cyclic group on three elements. A semidirect product is way of making a new group out of the transformations you can apply to another group. The symbol for a semidirect product looks like a standard multiplication x with the right side closed off. I'm too lazy to try to find that symbol in Unicode right now, and Deviant Art might not let me use it for a submission name anyway, so I just said XI was close enough.

I made the animation by first making a Python script to generate the image frames. I then imported each frame into The GIMP and used their animation features to turn it into a .gif. It was a bit tedious, but I wasn't in the mood to try to find a good open-source animation package, and I got a result in the end.