This effect is made possible with the detachCurve node in Maya. This is called the Detach Curves command in the Edit Curves menu. It is capable of cutting a curve into smaller sections. You need to specify the points along the curve before using it. By default it will create the new curves and delete the original, however by going into the commands options you can chose to 'keep original', which will leave the original curve unchanged and generate new curves with a connection to the original. With the detachCurve Node that is created, you can animate the points at which the curves are cut from, allowing you to create an animated curve, which follows the path of the original.
It is similar to how a motion path works, except rather than tracing a single point along the curve, you can trace a portion of the curve. As I said, it is completely procedural, meaning that the original curve can still be modified and the traced curve will update to any changes.
To create the final structure, I lofted between two copies of the traced curve, one of which was flattened, while the other remained 3D. Hopefully this video from a top down view shows what's going on.
Any thoughts on this?