I have enjoyed computational exploration of higher-dimensional and multipolar spaces.
Here is a draft overview of a number system that is the minimum nontrivial multipolar embedding of the complex plane and the real line it contains;
here is a more in-depth draft regarding multipolars, generalized inner product operations, and algebraic structures.

I have been credited with inventing the 4D visualization mode demonstrated in the video above.

Here is a fun simulator of central force potentials by Wolfgang Christian.