Advice for a bifurcating, oscilating plane

This is something I modeled quickly in tsplines and rhino to demonstrate what I wish to develop.  (This is the side view, perhaps the most informative).

It is an increasingly oscillating plane that then develops into a bifurcated mesh (2-D Voronoi like, yet with the continuing planar oscillations).

What components/plugins should I look into for research so that I can write such a definition?

If anyone has any instinctual rough ideas on how I can do this could you please write them down?

Thank you for your time.