Lacunary Möbius Fractals on the Unit Disk

Symmetry

DarinJ. Ulness¹  L.K. Mork²  Keith Sullivan³ 

[1] Department of Chemistry, Concordia College, Moorhead, MN 56562, USA;Department of Mathematics, Concordia College, Moorhead, MN 56562, USA;Department of Mathematics, University of Vermont, Burlington, VT 05405, USA;

关键词: fractals;    Julia sets;    Mandelbrot sets;    Möbius transformations;    lacunary function;    gap function;   

DOI  :  10.3390/sym13010091

来源: DOAJ

【 摘 要 】

Centered polygonal lacunary functions are a type of lacunary function that exhibit behaviors that set them apart from other lacunary functions, this includes rotational symmetry. This work will build off of earlier studies to incorporate the automorphism group of the open unit disk $\mathbb{D}$, which is a subgroup of the Möbius transformations. The behavior, dimension, dynamics, and sensitivity of filled-in Julia sets and Mandelbrot sets to variables will be discussed in detail. Additionally, several visualizations of this three-dimensional parameter space will be presented.

【 授权许可】

Unknown