OK, I promised more info on these screenshots:
They’re based on formulae found here for sound wave propagation through vibrating membranes. In fact, though, the QTZ I produced doesn’t really model natural phenomena, as I’m using a version of the formula for a rectangular plate, but driven by a polar coordinate system. I’ve also added an adjustable exponential multiplier to the rho coordinate (which represents each pixel’s distance from the centre of the texture), to make it look more interesting.
Finally managed to get a working video-grab of the effect in action.