I have written some code for rendering fractals (such as Julia or Mandelbrot) using Povray. Instead of separately rendering every single point, which makes the calculations very slow, I have implemented code that subdivides the image into sections that are calculated based on the information contained within them.

The algorithm is iterative. It starts at a level with low resolution, refining the mesh specifically in those parts of the image, where underlying structure is found.   For instance, only a minimal number of points is calculated in the homogeneous convergent region of the fractal. Homogeneous regions are rendered as a single big box. Thereby, a significant amount of calculation and rendering time is saved.

With povray, boxes or polygons are used to render the fractals. Thus, maximum resolution of the pictures is limited, since the number of objects gets very high at high resolutions. This issue will be addressed by implementing the code in C++, which should speed up things even more.