Inspiration

As usual, we wanted to build something useless (yet still aesthetic). As math students, the answer came naturally to us - an animation of orbits of Lie groups!

What it does

This site simulates the orbits of matrix Lie groups. For a fixed matrix and a few set starting points in 3d space, we compute the orbit of these points via the action of this matrix. This gives us a set of lines in 3d. Then, by varying the matrix, we can twist and warp these lines! We've provided several one-parameter variations for you to choose between, and you can even write your own matrices. Check out our live demo!

How we built it

We built this using the amazing 3D rendering three.js library, and otherwise pure Javascript/HTML/CSS.

Challenges we ran into

Some computations were very time and memory intensive, and we had to find ways to speed them up.

Accomplishments that we're proud of

We're very happy that these lines look so interesting!

What's next for Lie for Me

Make sharing custom matrix expressions easier by embedding it in the website link.

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