A short article by Ralph Griswold introducing the Morse-Thue (Thue-Morse) binary sequence and its history. It describes three ways to construct it (substitution map, append-complement, and binary digit reduction), its self-similarity and cube-free property, and generalization to other bases. It shows geometric interpretations in one, two and three dimensions and gives a two-shaft, two-treadle weaving draft derived from the sixth iteration of the Morse-Thue plane. References are included.