How could I create the curve which wraps around the torus to make this pattern? I know if I create one of the curves I can copy/paste to make the rest because they would be pretty much the same curve at different places on the torus.
your suggestions and advice would be very much appreciated!
I would get the circle that is the center line of the torus, then use Helix>AroundCurve and use the torus minor diameter as the helix diameter and 1 turn (or some other integral number if you want more twist) as the number of turns. Pipe the result if you want thickness, then a polar array around the torus center…
pretty much what was suggested already just with actual tubes which you can also twist 360 and flow.
for rendering real tubes may be interesting. excuse the ugly electric wire colors