This GeoNodes network simulates a curve advection based on a 3d noise texture.

The behaviour of the noise can be fully controlled via the parameters.

In this simulation, the curves not only grow, but they change constantly over time.

After the GeoNodes is a subdivision modifier for smoothing the meshed curves and keeping the simulation data small.

For more accuracy, you can deactivate the subdivision and increase the curve resolution. This prevents animation artifacts.