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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 contains no three consecutive identical blocks or no sub-block of the form awawa, where a is 0 or 1 and w is a binary block. The answer to these questions is positive. Thue proposes a binary sequence S generated by the following inflation rule:
Publication date: 
1 Jan 2014

Luigi Moretti, V Mozella

Biblio References: 
Pages: 179
Optics of aperiodic structures: fundamentals and device applications, Negro, LD, Editor