Using Geometry Nodes to make Concentric Rings, Where Each Ring is Slightly Different?

Question

I am working on an animation where rings grow from center in a pattern that is repeating, but where each ring has a slightly more distorted shape than the one before it.

I have managed to build a node system in GN that creates and distorts a ring (using noise), and I have managed to duplicate that ring a few times using math nodes that degrade each duplicate more than the one before it. But it is a lot of work, and I need the rings to be animated so that they grow beyond the frame as new ones continue to come in from center.

I know there is a way to do this but I'm having a hard time figuring out the following:

1. How to instance the initial ring, and have each instance deformed procedurally

2. How to make it so the inner edge of each subsequent ring takes on the shape of the outer edge of the ring that comes before it (currently I have the rings stacked so that the next ring is slightly smaller and the inner edge of the next ring has the illusion of also being the outer ring of the one before it, because the actual outer edge of the ring before it is hidden)

Is there a way to pull this off?

PROJECT FILE

This is the prototype I've made by manually creating each ring. Notice how each ring appears to share either an inner or outer edge with the next. Also notice how each ring has a slightly different shape than the next:

How can I set up the node tree so that this happens procedurally, without having to manually duplicate each ring?

These are my node setups:

Answer 1

Here's a setup where I first create a number of concentric circles with Duplicate Elements, then distort them with a noise node. Employing the Duplicate Index socket from the node allows you to sort the noise values into disparate batches for each circle so they can behave individually.

Harder part is creating the faces. Trying to extrude as edges is not very helpful. You could turn them into curves to use a Fill Curves node, but that would just create sequentially growing circles that overlap each other. We need to 'stitch' the circles at each gap between them. I usually do this by creating a Grid of faces in a single row/column, then moving its corner points to the circle vertex positions. Here's an older answer where I do a similar thing, with a more detailed explanation.

There's some index math going on there to achieve that result--it's basically manipulating the numbers so that the indices of the grid vertices match the circle vertices with the right indices (since each inner edge is used as a border for two faces, we can't just match them one-on-one). That's also the same reason why I'm using a flat Spiral at the beginning instead of simply a Mesh Circle: Spiral has split, double vertices at the start/end of its rotation and that extra vertex index helps with the stitching math.

Finally, before merging the overlapping vertices at the end, we capture the indices of each 'strip' using a Mesh Island node--since they aren't separate islands anymore after we merge them, we need to capture that information beforehand. Index information is then used in the Shader Editor to color the strips however you like.