Point displacement driven by noise, want tighter lines

I’m looking to achieve a look simillar to this in geometry nodes:

So far I tried many things by moving my instanced points on a grid but that didn’t really worked. That’s the closest I am getting to it with a noise texture:

I feel like I should edit the curve of the displacement vectors but I can’t find the node to do it properly, or where to put it.

Using a wave texture I get this:
Ideally, the point would all group up on the waves peaks.

Any ideas?

I know that the reference pic I have is generated with a mold algorithm, but the thing I look for is the grouping of the points.

This is what I could achieve, starting with a plane:

(Blender 3.1 alpha)point_distribution_noise.blend (104.3 KB)

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Oh I didn’t think about using it to distribute the points! That’s a good idea, thanks.