As an example of a T3D AVS parallel module, we developed a module which calculates the image of a mandelbrot set. The image is based on the iteration
where z and c are complex and 
. The values of c in the
complex plane for which 
is bounded as 
form the
interior of the set. The limit can be determined computationally
because it is known that if 
, then 
. An image of the mandelbrot set is created by assigning the
pixels in the image to a region in the complex plane. Each pixel
corresponds to a particular value for c for which the iteration is
performed until or an iteration limit is reached.
Exterior points which are distant from the set boundary diverge most
rapidly, while points in the interior reach the iteration limit.
Complex and colorful images of the set are obtained by using the
iteration count for each pixel as an index into a color map for the
pixel.