6mm dia bright mild steel can be cold-formed quite easily using wooden or metal jigs. Because it work-hardens slightly, it is easier to form smooth, constant radius bends than you might expect. Even a very simple tool (eg comprising a ~7mm dia hole in a piece of 1/2" thick steel plate, held in a bench vice) can allow you to make the bends you want in easy stages; friction will hold the work well enough as soon as you start to bend the 6mm rod; just make a slight bend, push the rod further through the hole, (and twist it slightly if you want the part to be a complex shape), another slight bend, and carry on. The closer together the bends are, and the more the steel work-hardens, the smoother the end result will be.
The ~7mm hole needs to be large enough to allow the curved rod through the hole and if necessary to withdraw the work. I would say that you will get enough leverage to bend 6mm rod provided you have a length to hold that is at least ~12" long. With practice you can make all kinds of 3D curves this way, whereas with many other methods you can most easily make curves in a single plane only, and you need a revised jig every time you want a different radius. With other types of jig the curves may be perfectly consistent; however for certain types of work, part of the charm of it is that the parts do vary slightly.
If you want to make the most complex shapes, it is often easiest to make simpler shapes and to weld them together; for example the 'S' shapes could be fabricated from two simpler 'C' shapes, which could be made using a fixed type jig.
cheers