Erik Curre's Video Artifact

Quaternion Fractal Animation

Click on the above hyperlink or the picture below to download the movie.

This movie was produced from 200 ray traced images. It depicts an animation of a mathematical object called a Julia set, which is a type of fractal. Normal two dimensional Julia sets are made with complex numbers, but my 3D version is done using a generalization of complex numbers called quaternions. What makes the fractal really interesting is that it is actually a 4D object. This is a problem because we can only perceive three spatial dimensions, not four. In order to render a 3D image on the computer screen, one must "slice" the 4D object with a three dimensional hyperplane. Then the points plotted on the screen are all the points that are in the intersection of the hyperplane and the fractal.

But one cannot get a good sense of what a 4D object is like simply by examining a single slice of the object. That would be like trying to understand a complex object like a human being just by looking at a two dimensional cross-section. Ideally, it would be nice to look at many slices of the fractal in order to get a better understanding of its nature.

And that's what my video artifact is all about. Each frame of animation is a different slice of the same 4D fractal object. The animation runs from -1.00 to 1.00 units along the axis of the slicing plane, in increments of 0.01 units per frame.

Think of this video as a mathematical tour of a higher dimension! Enjoy the video! I hope you like it. :-)

A high resolution rendering of a quaternion Julia set