English

Fractals Generated by Modifying Aperiodic Substitution Tilings

Metric Geometry 2023-05-19 v2

Abstract

This study proposes a method for producing an infinite number of fractals using aperiodic substitution tilings, exemplified by the Ammann Chair tiling. Higher-order substitutions of aperiodic tilings are utilized in relation to the Sierpinski carpet concept. The similarity dimensions of the fractals generated by the Ammann Chair tiling are calculated and shown to be dense. A fractal image generator was implemented in the Java programming language and is freely available for public use at https://github.com/KahHengLee/Ammann-Chair-Fractal.git

Keywords

Cite

@article{arxiv.2210.15465,
  title  = {Fractals Generated by Modifying Aperiodic Substitution Tilings},
  author = {Kah Heng Lee},
  journal= {arXiv preprint arXiv:2210.15465},
  year   = {2023}
}

Comments

10 pages, 12 figures

R2 v1 2026-06-28T04:38:53.249Z