Group Theory for Fun and Profit

Sometime earlier this year I started reading (for the third time) Conway’s book on quaternions and octonions. I never finished reading this book the previous times because I would get hooked with a specific topic mentioned there, do more research on that and never actually finish the book itself.

So that happened to me this time also. I started reading on symmetry groups, or wallpaper groups. Wallpaper groups are two dimensional repetitive patterns obtained by translations, rotations, reflections and glide reflections. As shown in Conway’s book, there are 17 different possible groups:

With the help of my collegue Bei we built a WebGL application that lets you create your own motifs and then apply the transformations of these 17 symmetry groups on your drawing. You can access the app here!.

Here’s a quick video that shows how to use it: