The binary sequence called the Thue–Morse (ThMo) sequence, or the Prouhet–Thue–Morse sequence, was introduced by Axel Thue (1863–1922), a Norwegian mathematician, in his seminal papers in 1906 and was rediscovered by Marston Morse in 1921. However, it was already implicit in a paper in 1851 by Prohuet. In his seminal papers in 1906 [1] and 1912 [2], Thue noted that any binary sequence of length≥ 4 must contain two consecutive identical blocks. He asked whether it is possible to find an infinite binary sequence that …