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.

中文翻译：

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单位磁盘上的LacunaryMöbius分形

居中的多边形基底函数是一种基底函数，其表现出将其与其他基底函数区分开的行为，这包括旋转对称性。这项工作将建立在早期研究的基础上，以合并开放单元磁盘的自同构组。$\mathbb{d}$，它是Möbius变换的子组。将详细讨论填充的Julia集和Mandelbrot集对变量的行为，尺寸，动力学和敏感性。此外，将展示此三维参数空间的几种可视化。