Visual Explanation of the Complexity in Julia Sets
| dc.contributor.author | Schrijvers, Okke | en_US |
| dc.contributor.author | Wijk, Jarke J. van | en_US |
| dc.contributor.editor | B. Preim, P. Rheingans, and H. Theisel | en_US |
| dc.date.accessioned | 2015-02-28T15:31:45Z | |
| dc.date.available | 2015-02-28T15:31:45Z | |
| dc.date.issued | 2013 | en_US |
| dc.description.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. | en_US |
| dc.description.seriesinformation | Computer Graphics Forum | en_US |
| dc.identifier.issn | 1467-8659 | en_US |
| dc.identifier.uri | https://doi.org/10.1111/cgf.12130 | en_US |
| dc.publisher | The Eurographics Association and Blackwell Publishing Ltd. | en_US |
| dc.subject | I.3.8 [Computer Graphics] | en_US |
| dc.subject | Applications | en_US |
| dc.title | Visual Explanation of the Complexity in Julia Sets | en_US |