I've been looking at the late paintings of Cy Twombly. He's known for his scratch and scrawl style of oil and mixed media paintings, which was quite influential. But his latest works add and even emphasize dripping as part of the aesthetic. This isn't an innovation, of course. Dripping has been a tool of abstract expressionism from the get go.
This got me to thinking about whether we can find a corollary to dripping in the other art forms. I'll assume that the key attribute here is that the drip is both controlled and uncontrolled. Here's what I came up with: The best analogy is the use of feedback in music performance. The feedback has a life of its own, emanating from the unintentional interplay of electronic technologies. (It's physics, and so is dripping.) What the musician does is try to shape that noise into something coherent or pleasing. Out-of-control feedback will drive an audience to ear-covering wincing in a flash, but controlled feedback can be beautiful. I'm thinking of Hendrix and Santana.