On Dendrites Generated By Symmetric Polygonal Systems: The Case of Regular Polygons

TL;DR

This paper investigates symmetric dendrites arising from polygonal systems with symmetry, establishing conditions under which their attractors are dendrites, especially focusing on regular polygons and zipper systems.

Contribution

It introduces the concept of G-symmetric polygonal systems and characterizes when their attractors form dendrites, advancing understanding of symmetric fractal structures.

Findings

Conditions for attractors to be dendrites

Characterization of symmetric dendrites in regular polygons

Analysis of zipper systems as attractors

Abstract

We define $G$-symmetric polygonal systems of similarities and study the properties of symmetric dendrites, which appear as their attractors. This allows us to find the conditions under which the attractor of a zipper becomes a dendrite.