Fractal tiles induced by tent maps
Dynamical Systems
2025-10-14 v3
Abstract
In the present article, we deal with geometrical objects induced by the tent maps associated with special Pisot numbers that we call tent-tiles. They are compact subsets of the one-, two-, or three-dimensional Euclidean space, depending on the particular special Pisot number. Most of the tent-tiles have a fractal shape and we study the Hausdorff dimension of their boundary. Furthermore, we are concerned with tilings induced by tent-tiles. It turns out that tent-tiles give rise to two types of lattice tilings. In order to obtain these results we establish and exploit connections between tent-tiles and Rauzy fractals induced by substitutions and automorphisms of the free group.
Keywords
Cite
@article{arxiv.2503.16790,
title = {Fractal tiles induced by tent maps},
author = {Klaus Scheicher and Victor F. Sirvent and Paul Surer},
journal= {arXiv preprint arXiv:2503.16790},
year = {2025}
}