Lipschitz equivalence of fractals and finite state automaton

2016/09/14 by Hui Rao, Rao, Hui, Yunjie Zhu +1
Computer Science · Mathematics · #26A16 #28A80 (Primary) #68Q45 (Secondary) #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:26A16 #msc:28A80 #msc:68Q45 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1609.04271

18 pages, 7 figures

arxiv created 2016/09/14 · openalex publication_date 2016/09/14 · arxiv updated 2016/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The study of Lipschitz equivalence of fractals is a very active topic in recent years. Most of the studies in literature concern totally disconnected fractals. In this paper, using finite state automata, we construct a bi-Lipschitz map between two fractal squares which are not totally disconnected. This is the first non-trivial map of this type. We also show that this map is measure-preserving.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.
• Lipschitz invariance of walk dimension on connected self-similar sets

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