We will create a fun computer game called "PathForms" with the goal of engaging the general public into learning mathematical concepts. Just as the "ColorTaiko!" project, it will be written using JavaScript and React.
The goal of this game is to visualize what is called Nielsen's algorithm in geometric group theory. In its classic definition, Nielsen's algorithm is stated in an unrevealing algebraic form. We will create a more visual, geometric way of describing and running Nielsen's algorithm: the game will draw a colored tree, and the player will be able to draw several paths in this tree and then to transform them by inverting some of the paths, moving the paths around and concatenating some of those paths. Each path is a sequence of colored edges in the tree,
and it can be equivalently viewed as a word, meaning a sequence of colors (=letters) together with orientations: this interpretation of the paths will also be displayed.
For the player, the first goal will be to do transformations to make the given paths
as short as possible. We expect to eventually implement several other versions of this game, with different goals.
For the students, this project is an opportunity to unleash their creativity. Feel free to look what kind of related illustrations are already available online. Make suggestions how the game should look and feel. We welcome any suggestions how to set up the game, what exactly it should do, its style, how to write the code, etc. And most importantly, have fun creating it.
The link to the game is also available from Igor Mineyev's math page.