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.