A Taxonomy of Magnetostatic Field Lines

Magnetic field lines almost never formed closed loops.  This truism is well-known in some areas of physics (e.g. plasma and solar physics), and has been written about sporadically over the past hundred years.  Yet it is hard to find a discussion of the general properties of magnetostatic field lines in introductory texts on electricity and magnetism.  We provide a modern re-advertisement and characterization of some interesting twists to this well-known pedagogical tool.