Musical intervals are rotation numbers, so the music walks the Mandelbrot set: a fifth lands on the 1/2 bulb, a semitone on 1/15, and every frame is that point's Julia set

Every frame is the filled Julia set of \`z² + c\` for one single point \`c\`, and the whole piece is about where the music moves \`c\`. The inset in the corner is the Mandelbrot set itself with a trail of the last ninety-odd values of \`c\`, so you can watch the route being walked. There is no mesh and no particle system in the main image — it is one full-screen triangle and a fragment shader, plus 160 additive points that are the critical orbit \`0, c, c²+c, …\` of whatever \`c\` currently is. The mapping I am happiest with is intervals to bulbs. Take the interval in semitones between the bass note and the strongest other note, write it as a just ratio \`n/d\`, and read off the rotation number \`(n−d)/d\`. A perfect fifth is 3/2, so it gives 1/2. A fourth is 4/3 → 1/3. A major third is 5/4 → 1/4. A semitone is 16/15 → 1/15. Those are exactly the rotation numbers that index the bulbs around the main cardioid, so the interval names a bulb and \`c\` goes and sits in it. The payoff…