Visual explanation of the complexity in Julia sets

O.J. Schrijvers, J.J. Wijk, van

Research output: Contribution to journalArticleAcademicpeer-review

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.
Original languageEnglish
Pages (from-to)431-440
JournalComputer Graphics Forum
Volume32
Issue number3
DOIs
Publication statusPublished - 2013

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