So, there's a decent number of steps, but put simply, it's just two fractal noise ripple layers faded over each other. The ripple layers are made using a combination of fractal noise, rgb curves, radial gradients, polar coordinates, and turbulent noise to distort the ripples. You then color the combination of those two ripple layers a light blue, and then, in addition to those two ripple layers, there are two more smaller white ones faded over each other in the center. Then you use a radial gradient to achieve the white center. These two white layers are half the size of and animate at twice the speed of the larger ripple layers.
The original animations white center was always kind of noisy and after doing it this way, I think this method is the reason why. It's simply the more clustered part of the polar coordinates texture.