"Dynamics of the Quaternion" is a raytraced animation of the quaternionic Julia set. The ray tracing method and the distance estimation formula are discussed in Ray Tracing Deterministic 3D Fractals (pdf). 
Rotated in the Complex Plane 11MB mpeg movie 
Section
Removed and Rotated 20MB mpeg movie 
Julia
Set FlyThrough 12MB mpeg movie 

The quaternions are a number system, which is the fourdimensional extension of the twodimensional complex number system. The image visualized in this movie is the quaternion extension of a single complex Julia set. This Julia set is rotated in the complex plane, an action that causes dynamic alterations to its quaternion extension. 
A section of the Julia set is removed to show two properties. First, the complex Julia set really does not change, and second, there always exists a set of perfect concentric circles centered at the origin embedded in the plane spanned by the imaginaries i and j. After the removed section is closed, the Julia set is rotated in the plane spanned by the real and j axes, and then rotated in the real and k axes. 
The set is next rotated through the complex plane. The dynamics of the Julia set are made more visible by a flythrough.
