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