Source: lcni.uoregon.edu/~mark/Geek_art/Simple_recursive_systems/Tesselations/Thue-Morse_tilings/Thue-Morse_tilings.html

‘There are several methods for constructing the sequence. One algorithm involves repeated concatenation;
{
Start with one symbol (a, or a black square) and concate its complementary symbol string (b, or a white square).
Repeat this complementary concatenation using the result as the input to the next repetion.
}
Another method is more general – a recursive symbol replacement system. Starting with ‘a’, replace ‘a’ with ‘a b’ and ‘b’ with ‘b a’, and then repeat these replacement rules indefinitely, always using the results as the input for the next generation.’