The ThueMorse(n, a, b) command generates the length-n prefix of the (infinite) Thue-Morse string, with initial values a and b. The arguments after the first are optional, and default to the strings  and , respectively.

The Thue-Morse string is the infinite string defined to be the fixed point of the iterated semigroup morphism  on the free semigroup generated by .

A recursive definition of the Thue-Morse sequence is as follows. , , .