A random curve on a lattice is chosen as described below. We move along the curve, playing two notes at once. Call the two notes L and R, because L will be played in the left channel and R will be played in the right channel. Every time we move left along the curve, L moves down one note in the scale, while every time we move right, L moves up one note in the scale. Likewise, every time we move up along the curve, R moves up one note, and every time we move down, R moves down one note. Listen on headphones to hear this best.

How did we choose the curve? First, we chose a random tree in a 9x9 grid (the tree is white in the movie, flashed at the start and shown at the end). This is called a random spanning tree. Then we surrounded the tree by a Peano-like curve. The colors of the curve reflect progress along the curve using hue, which is circular. This curve was then converted to music: the x-coordinates are in the left channel and the y-coordinates are in the right channel. The key is A major. The tree was chosen at random uniformly among all 8,326,627,661,691,818,545,121,844,900,397,056 possibilities. More information can be found at the website https:/rdlyons.pages.iu.edu/rw/rw.html You can also find a higher-quality video (vector-based graphics) there as a Flash (swf) file.

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