A tutorial on the visualization of forward orbits associated with Siegel disks in the quadratic Julia sets

Abstract

This article presents the use of computer graphics to gain a better understanding of the dynamics occurring in the Siegel disk Julia Sets. Traditional images of the Julia Sets usually display only the final behavior of the forward orbits of each point in the discretized complex plane. For each pixel in the image, a forward orbit must be computed—usually the information contained in the orbit is thrown away. This approach examines the orbit as well as its final behavior.