High Performance Iterated Function Systems

This article presents an implementation of the Fractal Flames algorithm. It uses CUDA and OpenGL to take advantage of the computational power of modern graphics cards. GPUs use a SIMT (Single Instruction Multiple Thread) architecture. It is needed to design programs in a way which avoids divergent branching. The Fractal Flames algorithm involves random function selection which needs to be calculated in each thread. The algorithm thus causes heavy branch divergence which leads toO(n) complexity in the number of functions. Current implementations suffer severely from this problem and address it by restricting the amount of functions to a value with acceptable computational overhead. The implementation presented in this paper changes the algorithm in a way that leads to O(1) complexity and therefore allows an arbitrary amount of active functions. This is done by applying a presorting algorithm that removes the random function selection and thus eliminates branch divergence completely.