2023/12/03 by Christoph Bandt · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algorithm #Artificial intelligence #Automaton #Cellular Automata and Applications #Cellular automaton #Combinatorics #Computability, Logic, AI Algorithms #Computer science #Fractal #Geometry #Mathematical analysis #Mathematics #Pure mathematics #Topological space #Topology (electrical circuits) #math.DS #math.MG #math.NT #msc:11A63 #msc:28A80 #msc:37B10 #msc:54B15 #msc:68Q45
paper · pdf · doi:10.46298/cm.12647
published in Communications in Mathematics Volume 33 (2025), Issue 2... (De Gruyter Open) · 33 pages, 14 figures
arxiv created 2024/06/14 · openalex publication_date 2024/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21 · arxiv updated 2026/08/05
Finite automata were used to determine multiple addresses in number systems and to find topological properties of self-affine tiles and finite type fractals. We join these two lines of research by axiomatically defining automata which generate topological spaces. Simple examples show the potential of the concept. Spaces generated by automata are topologically self-similar. Two basic algorithms are outlined. The first one determines automata for all k-tuples of equivalent addresses from the automaton for double addresses. The second one constructs finite topological spaces which approximate the generated space. Finally, we discuss the realization of automata-generated spaces as self-similar sets.