  Fractal image generation algorithms exhibit extreme parallelizability. Using
general purpose graphics processing unit (GPU) programming to implement
escape-time algorithms for Julia sets of functions,parallel methods generate
visually attractive fractal images much faster than traditional methods. Vastly
improved speeds are achieved using this method of computation, which allow
real-time generation and display of images. A comparison is made between
sequential and parallel implementations of the algorithm. An application
created by the authors demonstrates using the increased speed to create dynamic
imaging of fractals where the user may explore paths of parameter values
corresponding to a given function's Mandelbrot set. Examples are given of
artistic and mathematical insights gained by experiencing fractals
interactively and from the ability to sample the parameter space quickly and
comprehensively.
