Interactive Visualization of Quaternion Julia Sets
John C. Hart, Louis H. Kauffman, Daniel J. Sandin · 1990
The first half of a two-step quaternion Julia set visualization system is described. This step uses a quaternion square root function to adapt the classic inverse iteration algorithm to the quaternions. The augmented version produces a 3-D Julia set defined by a point cloud that can be interactively manipulated on a graphics workstation. Several cues are assigned to the point cloud to increase depth perception. Finally, a short theorem is proven that extends the domain of the inverse iteration method to a rotational family of quadratic quaternion Julia sets. 1 Introduction The first step of a two-part quaternion Julia set visualization process is presented. This step produces a point cloud defining the quaternion Julia set that can be manipulated in interactive time. The parameters investigated by this step are passed along to a parallel ray-tracing algorithm [3], the second step, that produces presentation quality renderings of quaternion Julia sets. Areas of interest in the ray-tra...