awesome work! If you get all configurations to be stable (maybe decrease the dt in addition to RK?) you can thank the scientists by sending a link to your work, I'll bet they'll be very happy with such pretty renderings.

That's some awesome work!

Hah, my high school memories - a graphical gravity simulator project for my CS class, leaking energy due to the use of a very naive integrator (the Euler method for ODEs).

You might want to try Stormer-Cowell, it's sort of a gold standard in orbit simulation.

UPDATED: Hmm, now that I think of it, this would probably profit more from a variable step method. Some of the close approaches seem to be really close for a fixed-step integrator.

This is very helpful, thanks! It's interesting to see how many 'near misses' there are in the new solutions (e.g. butterfly_1) -- a point that wasn't clear to me from the original plots.

Nice work. Have you seen the n-body configurations in this AMS article from a few years ago? http://www.ams.org/samplings/feature-column/fcarc-orbits1

I find it surprising that some configurations are as stable as they are with the simple integration method. At least (if I'm reading this correctly) you calculate positions and velocities at different times.

I really like you simulation.

Consider Bulirsch-Stoer.

https://en.wikipedia.org/wiki/Bulirsch%E2%80%93Stoer_algorit...

I know! We're so spoiled. I wanted to see WebGL animations of the real space orbits. Some nicely textured planets or something. All I got was an animated gif and the cheesey typewriter text thing. :-)

Seconded. Amusing terminal effects, but really poor visualization of the thing I actually care about, which is these new orbits. They should look into CDF or three.js