Recaman's Sequence (A005132).avi

This is the sequence made famous as the background music for the OEIS Movie. It sounds rather different here since it is played using the Golden Ratio base. It reminds me a bit of John Fahey: a basically repetitive pattern with subtle variations creeping in from different directions. Playing in Golden Ratio base means that each element of the sequence is mapped to a phinary numerical representation and then each '1' from this form is mapped to a note. The range of notes is wrapped around slightly asymmetrically with the "crease" at -1 shown at the left edge. Digits to the right of the radix point are then below and those to the left are shown above. One feature of Golden Ratio base is that the digits tend to be maximally separated. This tends to make the chords sound good without me having to know anything about music theory. Generally speaking, Fibonacci numbers and the golden ratio may plausibly be involved in the analysis of an kind of separation phenomena. The distances between leaves on plants is a well known example. Stress patterns in words and phrases and socially acceptible speaking speaking distances are also separation problems Would Fibonacci numbers and the golden ratio be useful for understanding these phenomena? One odd thing I've noticed is that it often appears that one of the color bars is standing still, and the others are dancing around this one. Any explanations?