What a fascinating question: can you create a sequence without any repetition? Randomness won’t do, since clumping will occur. It turns out that finding non-repeating sequences has important applications to sonar. If there’s any repetition in the sequence of sounds transmitted, when the signal returns, parts of the signal can be confused because there’s internal similarity. Watch the talk for the whole story, and enjoy the ‘ugliest piece of music’ at the end! 🙂