https://www.threebodyorbits.com/hunt
Also thank you so much for all the positive feedback, I truly appreciate it. If you have any additional suggestions please let me know
I have a quick question: how are you currently checking if a new candidate is genuinely novel rather than a rotated, time-shifted, or rescaled duplicate of an existing solution?
If you are not already computing it, topological classification (mapping orbits to free group words) would be a great way to quickly prune duplicates before heavy numerical checks, and it's also really useful metadata to display in the atlas itself. Also, showing shape sphere projections of the orbits would be a nice visual addition.
After you sent your question I noticed an issue with the "hunt" settings. Orbit novelty was not properly assessed, and it just kept re-discovering already existing orbit families. I updated the search based on your suggestions and just submitted an update that now checks candidates like this:
- Does the motion really repeat? An independent more high precision periodicity check is performed to confirm that bodies truly return to their starting positions and velocities - Is it a different form of an existing orbit? Compares against reference orbits from the atlas, allowing for rotation, different starting points in time, rescaling, reflection, and relabeling of bodies -Is it just the same orbit traced several times? Checks for shorter repeated periods -Now topological information is taken into account as well. In the current version, I use reduced syzygy sequences that record which body is in the middle whenever the three bodies are lined up. This was easier to implement than the familiar a, b, A, B notation.
Also, new candidates here are not automatically declared as new discoveries. They will undergo additional validation before they are added to the atlas.
The shape-sphere suggestion sounds great - would you suggest adding this to the "hunt" page, or to every orbit in the atlas?
For anyone else interested in the math behind the shape sphere coordinates and topological free group classification, I put together an agent skill with code examples here: https://github.com/suvakov/vibes/blob/main/skills/shape_sphe...