Thank you again everyone for your help.
Based on your guidance I have something close.
A few notes:
I'm using a depth map pass to have the lines farther away fade off.
I tried using a sweep nurb to create the geometry, but the Displacer would flatten it in areas and it would lose that uniform graphic look. I ended up using hair to get an undistorted line.
Big challenge:
If you look at the reference image at the very top of the thread, the wavy lines twist and curl at points. It's fine if I cannot use circle splines any longer and it's 2 half arcs or whatever as a cheat, because if you look at the reference, there is room for that.
Any ideas would be welcomed. I've played around with the Bend and Twist deformer a bit but feel a little stuck.
I'll gladly buy anyone of Coke if they have a solve, meaning, a $100 Venmo/Paypal. : )
Wave_Test_01.mp4
Wave_Test.c4d