Visual Explanation of the Complexity in Julia Sets

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Date
2013
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd.
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.
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@article{
10.1111:cgf.12130
, journal = {Computer Graphics Forum}, title = {{
Visual Explanation of the Complexity in Julia Sets
}}, author = {
Schrijvers, Okke
 and
Wijk, Jarke J. van
}, year = {
2013
}, publisher = {
The Eurographics Association and Blackwell Publishing Ltd.
}, ISSN = {
1467-8659
}, DOI = {
10.1111/cgf.12130
} }
Citation