Fractals Generated by Modifying Aperiodic Substitution Tilings

2022/10/18 by Lee, Kah Heng
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2210.15465

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

Related

• An aperiodic tiling made of one tile, a triangle
• Development of an Algorithm for Constructing Complex Fractal Images using Geometric Substitutions from Fractals Generated by the L-systems Method
• Tensor-generated fractals: Using tensor decompositions for creating self-similar patterns
• Combinatorics of a fractal tiling family
• Hinged Truchet tiling fractals