As the default simulation played out beautifully on-load, I immediately started to question: "hang on, I thought there wasn't a solution for 3 bodies, but this looks stable".

Before I could complete the thought, it fell apart magnificently :)

The default configuration is a special case. They are all in a stable orbit around the common barycenter, always forming an equilateral triangle. We actually have closed form solutions for this kind of configuration.

See https://en.wikipedia.org/wiki/Three-body_problem#General_sol...

There are quite a few solutions ;)

https://www.sciencealert.com/we-just-got-12000-new-solutions...