Real Time Visualization of Chaotic Functions

Fractals are a fundamental natural structure that has fascinated the sci- entific community for a long time. To allow for better understanding of fractals, visualization techniques can be used. The focus of this thesis is real-time rendering of fractals that are similar to the Mandelbrot set or the Newton fractal. Detailed exploration of these fractals is complicated due to their recursive-manner which leads to the fact that rendering them is com- putationally demanding. Existing solutions do not work in real-time or have low visual quality. We want to change that and allow high-quality real- time rendering. During our analysis of the problem, we generalize fractals to chaotic functions. To achieve high-quality rendering with low overhead, we introduce a method for adaptive super-sampling of chaotic functions. To achieve real-time performance, we show how to use sample reuse, foveated rendering, and other techniques. We implement a parallel, GPU-based, high- quality renderer that runs in real-time and produces visually-attractive views of given fractals. The program can visualize any given chaotic function. This way, we open the realm of real-time visualization of chaotic functions to the public and lay a basis for future research.