About Upside-down Exponential Slow:

This mode is closely related to Exponential Slow, and is also based on the famous Thue-Morse sequence. But the terms in the sequence are turned on their heads a little bit; the order of each exponential grouping of terms (i.e. 2 terms, 4 terms, 8 terms, 16 terms, etc.) is reversed! Thus, this sequences begins: 1, 0, 1, 0, 2, 1, 1, 0, 3, 2, 2, 1, 2, 1, 1, 0, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0...

While the nth term of Exponential Slow is equal to the number of times the digit 1 appears in the binary representation of n, the nth term of Upside-Down Exponential Slow is equal to the number of times the digit 0 appears in the binary representation of n. For instance, for the 8th term, n = 8. It's binary representation is 1000, which has three 0s in it, so the term is 3. (For the first term in the sequence, n=0.)

Like Exponential Slow, Upside-Down Exponential Slow 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 this one, you end up with exactly the same sequence!

Because of this self-similarity, it "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 A023416.