Again, a binary star system, with what at first appears to be a single point mass (a small asteroid, say).
But in fact, the simulation starts with two point masses, separated by only about one kilometre (an insignificant distance in astronomical terms). The interest here is to see whether these bodies will stay together. This is a demonstration of "sensitive dependence on initial conditions" which is characteristic of chaos.
You'll need to run this simulation for more than 1000 simulated days before you start to see the two asteroids really separate, ultimately to the extent that they have very different destinies. Some interesting things happen along the way! Run it to about 3000 simulated days for the full story.