Looks like my main pet GR project is about to enter something akin to maintenance mode, since it now does all I currently need it to. It's nothing earth-shattering at first glance, but is very concise (e.g. ~100 lines of Python for the simulator script) and should be easier to understand than most simulation sources that I have seen ;) I can't really give any visuals here, but I think the way it is implemented is seriously neat, and not published anywhere as far as I know. It works for particle and light orbits (spherical and "spherical shell", including polar), and even has an initial conditions generator script. To run it you will need a Linux box (tested on Debian Wheezy & Ubuntu Trusty) or virtual machine (VirtualBox works), and also need to be used to executing shell scripts. The README in the project lists dependencies and some example commands to get you started. Here is the project (this one is BSD licenced), and here is a little paper/technical note that I knocked up to try to explain what's going on under the covers. Hope someone out there finds it useful . . .