This a screenshot of an OpenGL program I wrote in my spare time during my undergraduate course to draw scenes with special-relativistic effects.
In this scene the spheres are orbiting clockwise around the centre sphere which is stationary (relative to the camera). The scene is illuminated with two black-body lights from behind the camera, and one green light from the top to show off the Doppler effect (red and blue shift).
If you are interested I have put the program on GitHub.
I've really done a similar thing. The main inspiration for me was my special relativity class at university. I have done my lighting differently to a A Slower Speed of Light, because I've used spectrums instead of RGB: I found this stack exchange answer afterwards which outlines why that makes more sense.