2015/12/06 by Hassan Douzi, Douzi, Hassan
Computer Science · Materials Science · Mathematics · #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.1512.01785
openalex publication_date 2015/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.