[noebihlc] rendering 3D fractals

consider rendering a 3D fractal like the Mandelbulb.

a fractal has details smaller than the eye can directly see.  however, fine structure can cause diffraction effects that the eye can see.  such effects will probably be challenging (computationally expensive) to render: light is a wave, not a particle.  are the diffraction effects interesting?

coat the fractal with a transparent material of constant thickness and positive refractive index, then ray-trace.  although a tiny structure in the fractal might be too small to see, we can see that something is there by how its surrounding volume distorts light.  this was inspired by escape-time coloring of 2D fractals: stuff outside the fractal catches the eye.

the surrounding transparent material should probably have no reflectivity to avoid confusing reflections.  however, a transparent but unreflective material might itself be confusing because such materials do not exist in the real world.  we especially don't see things that remain nonreflective even at glancing angles.

fancier: refractive index depends on distance or escape time.  but this might be too complicated for people to visually understand what is going on.  ray tracing with continuously varying refractive index will also be challenging.