# Russell Lyons

Originally inspired by amazing graphics and videos at a math
conference I attended, I decided to illustrate some basic concepts
in my research area, both for the book I am writing and in order to
increase interest in mathematics among students. After making some
such graphics and small animated gifs, I realized that music could
help make vivid the motion of random walks. I chose a very simple
and natural way to turn walks into music. Surprisingly, no one had
done this before. Even more astonishing was that the music was
pleasing as music. Thus, I extended this idea and turned the Peano
curve surrounding a UST into music in the same way. Hue, a circular
color scale, was used to illustrate visually the progress along the
closed curve, matching the musical progress. A score is at
http://pages.iu.edu/~rdlyons/rw/peano9.pdf. A limit of the Peano
curve as the mesh tends to 0 is a random space-filling curve that is
described by the Schramm-Loewner Evolution, a major part of
probability.