I have something similar at https://gravitoy.xyz
With it I have discovered up to 11-dimensional choreographies, see https://lycium.github.io/hyperchoreography/ and code at https://github.com/lycium/hyperchoreography/
Exposition video: https://youtube.com/watch?v=sIfff10hYZA
Example rendered output from Gravitoy (not of a choreography though): https://www.youtube.com/watch?v=N3BwCoiwsGk
Looks like I need to update my catalogue to take into account the many different 2D choreographies from the references on this site!
That Pythagorean one with the ejection is cool. I wonder whether you could use it to accelerate a spacecraft.
Cool, are any of these particularly stable? Like, is there any choreography that could plausibly survive in practice?
Most of them are extremely unstable, which is what the Morse number encodes - the number of directions you can roll down doing action minimisation. I don't think any N-body choreographies can exist in nature, because it requires point masses, exactly equal masses, Newtonian gravity etc.
BTW, I've wondered if it's possible to have N-body choreographies in general relativity; maybe some brave person can explore that :)