I have successfully implemented a realtime Julia/Mandelbrot set generator on the GPU. Primarily out of curiosity, what I'm looking for now is a faster test algorithm.
Ideally, I want a boolean function that would tell whether a point is within the set. This is currently performed in the classic way with a bunch of iterations (maybe 100 or 1,000, or more). On the GPU, which doesn't like branching code, this is problematic.
I'm speculating that because the Julia/Mandelbrot Sets are infinitely complex, no constant time algorithm can give such an answer. However, I'm hoping that there are at least faster algorithms. I don't care about convergence rate information--just a simple yes/no function is all that is needed.