About Exponential Slow:

This mode is based on the famous Thue-Morse number sequence, which begins like this: 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5...

Thue-Morse can be computed in many ways; one of the easiest ways to find the nth term is to simply count the number of times the digit 1 appears in the binary representation of n. For instance, for the 11th term, n = 11. It's binary representation is 1011, in which the digit 1 occurs three times, so the term is 3. (For the first term in the sequence, n=0.)

Thue-Morse is also a self-similar integer sequence; it contains infinitely many copies of itself and is invariant under scale. If you create a new integer sequence by using every alternate term of Thue-Morse, you end up with exactly the same sequence!

Because of this self-similarity, Thue-Morse "slows down" exponentially as it goes on. It takes longer and longer for "new" numbers to appear as terms. Correspondingly, it takes longer and longer to move forward in the audio file you have selected.

To switch the musical structure to this mode, click on the Change button.

Reference: N. J. A. Sloane, editor (2002), The On-Line Encyclopedia of Integer Sequences, published electronically at http://www.research.att.com/~njas/sequences. Sequence A000120.