Combinatorics of a fractal tiling family
Combinatorics
2023-09-18 v1
Abstract
In this paper, we propose to enumerate all different configurations belonging to a specific class of fractals: A binary initial tile is selected and a finite recursive tiling process is engaged to produce auto-similar binary patterns. For each initial tile choice the number of possible configurations is finite. This combinatorial problem recalls the famous Escher tiling problem [2]. By using the Burnside lemma we show that there are exactly 232 really different fractals when the initial tile is a particular 2x2 matrix. Partial results are also presented in the 3x3 case when the initial tile presents some symmetry properties.
Keywords
Cite
@article{arxiv.1512.01785,
title = {Combinatorics of a fractal tiling family},
author = {Hassan Douzi},
journal= {arXiv preprint arXiv:1512.01785},
year = {2023}
}