I thought I would share this little writeup on a project I'm quite proud of. The code can be found on GitHub [0]. This article is mostly about the implementation of the simulation in Haskell. I've also written another article [1] on the physics of the simulation. It should be approachable even for those without any general relativity background.
[0] https://github.com/flannelhead/blackstar
[1] https://flannelhead.github.io/posts/2016-03-06-photons-and-b...
One idea that you might think about adding is redshifting the light that comes off the accretion disk. If the light is monochromatic coming off the disk, then the areas of the disk closer to the horizon should look more red to a distant observer.
The physical explanation of an accretion disk would be some matter that is orbiting the black hole and emitting radiation, so it makes some sense at least. https://en.wikipedia.org/wiki/Accretion_disk
A comparison between different integrators is in the plans. It would be certainly interesting to try e.g. velocity Verlet and some other symplectic integrators.
[0] https://en.wikipedia.org/wiki/Gravitational_lens#Explanation... [1] http://spiro.fisica.unipd.it/~antonell/schwarzschild/