A while back I stumbled upon a neat Processing sketch that dealt with the production of electromagnetic field lines in an unusual way (credit to bitcraft). In the past I've approached this sort of thing through vector field integration, where streamlines are represented as paths of moving particles. The sketch above takes a different approach however. Each pixel is given a scalar value based on the weighted angle sum of vectors coming from each charge. This field can then be contoured however you like. Stream lines, for example, can be extracted by isolating pixels that lie on given thresholds. The fun thing about this approach is that when translated to 3d it produces stream surfaces instead of stream lines.
Platforms: C#, Grasshopper, Rhino