Surface deformation from multiple curves

So essentially i’ve got a pattern derived from drawing out curves and i’m looking at taking those curves and deforming a surface in order to create a pattern/texture over that surface, similar to this reference image.

Curves ATM:

Reference image aesthetic im wanting to achieve.

I’ve tried a few methods, curve from closest point etc with little success, I kind of just need a pointer in which direction to move - is it a matter of having too many curves?

Appreciate it if someone can point me in the right direction or can show me where to look for more information.

THanks. (50.3 KB)

Actually, I’m somewhat getting there.

Though i still wonder if there better ways, or something thats more sharper defined