The initial configuration of the link as seen above was produced in two steps. First the five concentric rings were constructed. KnotPlot has facilities to do such operations easily. The only tricky part was sketching in 3D the last component of the link, which goes over and under the concentric rings in a complicated sort of way. This construction was originally due to the mathematician H. Brunn in the late nineteenth century. It is also illustrated on page 67 of Dale Rolfsen's book Knots and Links.
The following sequence shows how the link on the front cover evolves from the initial configuration by applying a simple dynamical system to the "beads" (which are the yellow spheres in the above picture).