"Dynamics of the Quaternion" is a ray-traced animation of the quaternionic Julia set. The ray- tracing method and the distance estimation formula are discussed in Ray Tracing Deterministic 3-D Fractals (pdf).
Rotated in the Complex Plane

11MB mpeg movie
Section Removed and Rotated

20MB mpeg movie
Julia Set Fly-Through

12MB mpeg movie
The quaternions are a number system, which is the four-dimensional extension of the two-dimensional 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 fly-through.
Dynamics of the Quaternion, 1989
Computer Animation: John Hart


Tom DeFanti
Louis Kauffman
Alan Norton
Daniel Sandin

Tech Directors:

Fred Dech
Irving Moy

Executive Producers

Maxine Brown
Tom DeFanti
Daniel Sandin