Basically I'm working with a hi-res ground plane as water. I have a flower floating on the water, and I want to have circular ripples coming from the flower. It's a closeup, but I still want the ripples to become shallower and farther apart as they move out from the center, as in this photograph of a water ripple. The more images of rippling water I look at, the more I see that it's not so much that they are steadily farther apart as they move away from the center as that there is a big variation around the object itself with some very wide rings and some narrower, and then they even out and get smaller the farther they are from the center. So it would seem I would have to introduce some sort of distortion to allow me to put some variability there, somehow? But they all graduate to shallower height as they move from the center, and fade out, so that you don't see them at all after a distance from the center.

If I use the wave texture node, I get a center circle with surrounding circles that all get smaller until they reach a uniform size as they move away from the center, like so:

I just want to make that look more natural by giving it some variability (not the distortion that's in the node, that just makes it wiggly but does nothing to change the frequency) and making it fade out the farther from the center it moves.

I wonder if I am putting too much confidence in math's ability to do stuff like that, I know there are some things that you just can't do really well with procedural nodes, like super realistic wood grain. If there's a way to do it with nodes I want to learn, but I can accept if I'm better off just painting a height map.