Thue-Morse Sequence

Generates the Prouhet-Thue-Morse sequence, a well-known binary sequence defined by its recursive structure. The tool allows users to input parameters to determine the length or specific indices of the desired sequence, calculating the pattern based on the parity of the number of ones in the binary representation of the index. It iteratively builds the sequence such that every block of $N$ bits contains an equal number of zeros and ones, exhibiting distinct self-similarity properties across different scales. Researchers in mathematics, computer science, and theoretical physics utilize this generator for studying pseudorandom sequences and combinatorics. Students can use it to understand fundamental concepts in discrete mathematics, while developers might apply the generated sequence pattern when testing algorithms or exploring data structures that require highly balanced binary inputs.