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 curvs not only grow, but they change constantly over time.

After the GeoNodes is a subvisision modifier for smoothing the meshed curvs and keeping the simulation data small.

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