Perhaps interestingly this visualisation technically depicts only half of the Fourier transform. The full transform adds the exact mirror image of each circle to cancel out the horizontal movement (which is usually drawn vertically, but this visualization swaps the real and imaginary axes).
This means that what this visualisation effectively depicts is the analytical signal [1] which is what you get when you use the hilbert transform to 'recover' the imaginary part of the original signal. This transformation is convenient as it allows you to determine the instantaneous phase and amplitude at each point in time, so you can calculate a frequency and volume for every single moment in time.