I've been experimenting with the chaotic Gaspard-Rice system as described in this article:
https://en.wikipedia.org/wiki/Chaotic_scattering

I think it might be possible to derive some kind of fractal structure out of it but so far I've had no success.  I've made a color map by assigning each point a vector pointing at the scatterer at an angle dependent on the position of the point.  There's a variety of ways to do this and each way corresponds to a vector field.  In the plots below I've used a standard rotating one around the origin one.  The color depends on the length of the ray before it escapes the system.

Linkback: https://fractalforums.org/off-topic/29/chaotic-scattering/950/