Editing Thue–Morse sequence (section)

{{Short description|Infinite binary sequence generated by repeated complementation and concatenation}}
[[Image:Morse-Thue sequence.gif|frame|right|This graphic demonstrates the repeating and complementary makeup of the Thue–Morse sequence.]]
In [[mathematics]], the '''Thue–Morse''' or '''Prouhet–Thue–Morse sequence''' is the [[binary sequence]] (an infinite sequence of 0s and 1s) that can be obtained by starting with 0 and successively appending the [[Boolean algebra|Boolean complement]] of the sequence obtained thus far.<ref name=A010060>{{Cite OEIS|A010060|Thue-Morse sequence}}</ref> It is sometimes called the '''fair share sequence''' because of its applications to [[fair division]] or '''parity sequence'''. The first few steps of this procedure yield the strings 0, 01, 0110, 01101001, 0110100110010110, and so on, which are the [[prefix (mathematics)|prefixes]] of the Thue–Morse sequence. The full sequence begins:

:01101001100101101001011001101001....<ref name=A010060 />

The sequence is named after [[Axel Thue]], [[Marston Morse]] and (in its extended form) [[Eugène Prouhet]].