2005/08/22 by Jun Ma, Judy A. Holdener · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Advanced Mathematical Theories and Applications #Mathematics and Applications #Koch snowflake #Morse code #Mathematics #Snowflake #Sequence (biology) #Plane (geometry) #Polygon (computer graphics) #Combinatorics #Geometry #Mathematical analysis #Fractal #Computer science #Physics
paper · doi:10.1142/s0218348x05002908
openalex publication_date 2005/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26
In this paper, we reveal a remarkable connection between the Thue-Morse sequence and the Koch snowflake. Using turtle geometry and polygon maps, we realize the Thue-Morse sequence as the limit of polygonal curves in the plane. We then prove that a sequence of such curves converges to the Koch snowflake in the Hausdorff metric. In the final section we consider generalized Thue-Morse sequences and provide a characterization of those that encode curves converging to the Koch snowflake.