The Thue-Morse constant, also known as the parity constant, the number defined as follows: Take a string of 1's and 0's and follow it by its complement (the same string with 1's switched to 0's and vice versa) to give a string twice as long. Repeat this process forever (starting with 0 as the initial string) to get the sequence 011 010 011 001 011 010 010 110.... Make this a binary fraction, 0.011 010 011 001 011 0...2, and rewrite it in base 10. The resulting transcendental number, 0.412 454 033 64..., is the Thue-Morse constant.