This solution of the 3-body problem is stable, apparently: twitter.com/simon_tardivel…

Assuming its not a numerical issue, I am not sure I understand why symmetry should fall apart.

If it's not perfectly symmetrical at the start, it can become extremely asymmetric later. Or maybe it's symmetrical at the start but the numerical errors are asymmetric for some reason. In the real world, outside influences can introduce the asymmetry.

I don't understand why it's unstable. I'm the farthest thing from a physicist, so I'm sure I'm missing something obviously, but it seems to me like it should be stable. Is something influencing their movement besides each other?

Lots of systems are unstable, and then they can *look* like they're doing something simple, but in reality they're not quite, and the deviation from simple behavior gradually builds up over time and suddenly spirals out of control. Just solve the equations...

does this have some nice 4d interpretation like you wrote about 2 body problem?

I doubt it! The gravitational 2-body problem is very special in having a secret 4-dimensional rotation symmetry. johncarlosbaez.wordpress.com/2015/03/17/pla…

How can we say this isn't the result of a numerical rounding error in the integration script breaking the symmetry? Did someone try reproducing this result?

It's either the result of a numerical rounding error, or a deliberately introduced imperfection in the initial conditions. It doesn't really matter much: either way, a slight deviation from symmetry is getting amplified.

Is the author using floating point for this simulation?

I don't know. Are you, @simon_tardivel ? Either numerical errors or deliberate errors introduced into the initial conditions are being amplified by the instability of this trajectory.