What are some uses of the Thue-Morse sequence in computer science?

Note: I come from a mathematics background.

The Thue-Morse sequence $$t_n$$ is a binary sequence that takes the value $$0$$ at the positive integer $$n$$ if the number of $$1$$s in its binary expansion is even, $$1$$ otherwise.

A definition that is closer to computer science states that $$t_n$$ is the binary sequence obtained by starting with $$0$$ and successively appending the boolean complement of the sequence obtained so far.

Thus, $$t_n$$ begins $$0,1,1,0,1,0,0,1,\ldots$$

This sequence is of much interest in mathematics, but so far I have not come across any applications in computer science. This surprises me, for the two following reasons:

• The Thue-Morse sequence is automatic, i.e., the sequence is fully characterized by a finite automaton,
• It is a binary sequence.

What theoretic or practical applications of the Thue-Morse sequence are there in computer science?