Towards realistic modeling and rendering of 3-D escape-time deterministic fractal shapes

An escape-time method was introduced to generate the images of Julia and Mandelbrot sets and has been applied to visualize attractors of iterated function systems (IFS). Rendering deterministic fractal shapes by IFS escape-time methods suffer from some problems: the intersection of a ray with a fractal surface is not easy, surface normals are undefined, and the object aliases at all sampling resolutions. We propose a method called direct continuous escape-time for rendering deterministic fractals and attempt to recover these rendering problems in a reasonable time. The simple representation and the speed of computation of our algorithm makes rendering deterministic fractals reliable for interactive machines.