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.

Thanks! I did not know Stormer-Cowell, but googling it, I've found a comparision to DROMO, suggesting that it's even more stable: http://www.congrex.nl/11c01proceedings/Papers/2225317%20Pela...

I'll try both if I find the time :)

Heh, that's exactly what I made with a friend for a physics project in high school. We didn't even consider different methods--we used the Euler method because it's the most intuitive. I didn't even know it had a name!

Good times.

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.

I don't know much about this domain, but I wonder if these close approaches make it less likely that the associated orbit is stable over long times?

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

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.

Consider Bulirsch-Stoer.

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

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.

That's some awesome work!