3D gradient ribbon

Pre-compose a layer with a shape layer and your purple path, animate the path as needed, apply a CC Force Motion Blue in the parent comp and crank up the motion blur samples. Using multiple shapes as the catus advised may also help. Otherwise this is stuff for plug-ins like Trapcode TAO, MIR, Form or Plexus.

Mylenium

I've made something similar before, use a shape layer with out a fill, use a stroke to create the initial shape, then use a Repeater to create multiple copies, changing the position data so that the duplicates are very close together, but then set each's opacity to 99%, this will cause the further duplicates to fade out.  Finally, you might want to drop a blur on to completely blend the copies together.