Visual Explanation of the Complexity in Julia Sets. (1st July 2013)

• Record Type: Journal Article
• Authors: Schrijvers, Okke; van Wijk, Jarke J.
• Is Part Of: Computer graphics forum. Volume 32:Number 3(2013)Part 4
• Page Start: 431
• Page End: 440
• Publication Date: 2013-07-01
• Subjects: I.3.8 [Computer Graphics]: Applications; Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.12130
• Languages: English
• ISSNs: 0167-7055

Abstract

Abstract: Julia sets based on quadratic polynomials have a very simple definition, yet a highly intricate shape. Our contribution is to provide a visual explanation for this complexity. To this end we show the construction of Julia sets as a dynamic process, in contrast to showing just a static image of the set itself. Our method is based on the Inverse Iteration Method (IIM). We start with a disk, which is successively distorted. The crucial step is to show an animation of the effect of taking a root of a subset of the complex plane. We present four different approaches for this, using a Riemann surface, a corkscrew, a fan, and disks as metaphors. We packaged our results in an interactive tool with a simple interface, such that everybody can view and inspect these for different Julia sets. The results are useful for teaching complex analysis, promoting mathematics, entertainment, and, above all, as a visual explanation for the complexity of Julia sets.