Thue-Morse Sequence

The Thue-Morse sequence is a specific pattern of zeros and ones generated by starting with 0 and then repeatedly appending the bitwise negation (flipping zeros to ones and vice versa) of the sequence so far. This creates a self-similar, infinite sequence without repeating patterns of certain lengths. It has interesting mathematical properties, such as avoiding cubes (three identical blocks in a row) and appearing in various areas like combinatorics, computer science, and chaos theory. The sequence can be constructed by a simple rule based on the binary representation of numbers or by iterative application of the negation process.