We visted some friends yesterday. They showed us a math movie about fractals and the Mandelbrot Set. Sounds dull, but these things are actually very beautiful.
One of the talking heads interviewed defined a fractal as a form, which no matter how many times it was magnified, always contained a further level of fine detail. Furthermore, the details look rather similar, but not necessarily identical at any level of magnification. The classic example of this is called the Mandelbrot Set, which looks rather like a bug, but on further magnification reveals startlingly beautiful detail.
The mathemusician in me immediately thought of piobaireachd. A simple tune, but the further you play, the more complex it becomes. Of course, the tunes end and fractals never do, but I like how formulaic and yet random both are. I’m sure I’m not the first person to notice this. I think I will post on the piping boards and report back.