We define the Thue–Morse morphism to be the function "f" from the set of binary sequences to itself by replacing every 0 in a sequence with 01 and every 1 with 10. Then if "T" is the Thue–Morse sequence, then "f"("T") is "T" again; that is, "T" is a fixed point of "f". The function "f" is a prolongable morphism on the free monoid {0,1}∗ with "T" as fixed point: indeed, "T" is essentially the "only" fixed point of "f"; the only other fixed point is the bitwise negation of "T", which is simply the Thue–Morse sequence on (1,0) instead of on (0,1). This property may be generalized to the concept of an automatic sequence.