GENERALIZED THUE-MORSE SEQUENCES AND THE VON KOCH CURVE
: In a recent paper, Ma and Holdener used turtle geometry and polygon maps to show that the Thue-Morse sequence encodes the von Koch curve. In the ﬁnal paragraph of this same paper, they ask whether or not there exist certain generalized Thue-Morse sequences that also encode the curve. Here we answer this question in the aﬃrmative, providing an inﬁnite family of words that generate generalized Thue-Morse sequences encoding the von Koch curve.
"Generalized Thue-Morse sequences and the von Koch Curve," to appear in the International Journal of Pure and Applied Mathematics (co-authored with Kenyon students Lee Kennard '07 and Matthew Zaremsky '07
International Journal of Pure and Applied Mathematics