This might be bit of a tangent but this is one of the problems where it matters which parameter you are looking for.
While it is a O(n!) in relation to reflections a real physical rendering is 'mere' O(n) in relation to volume (or n^3 in relation to the sides of the cubic volume we want to simulate)! Why? We simply create a grid of around 200nm volumes and run a wave simulation for the light. Or O(nlogn) if we want to use fft based simulation.
Naturally this consumes horrendous amounts of memory and computational power simply because the size of spaces humans are interested in are so massive compared to wavelength of light.
But eventually we might move into this direction, maybe we even live to see it eventually.
While it is a O(n!) in relation to reflections a real physical rendering is 'mere' O(n) in relation to volume (or n^3 in relation to the sides of the cubic volume we want to simulate)! Why? We simply create a grid of around 200nm volumes and run a wave simulation for the light. Or O(nlogn) if we want to use fft based simulation.
Naturally this consumes horrendous amounts of memory and computational power simply because the size of spaces humans are interested in are so massive compared to wavelength of light.
But eventually we might move into this direction, maybe we even live to see it eventually.