They are basically visualizations of the "integral curves" defined by the vector field. https://en.wikipedia.org/wiki/Integral_curve https://en.wikipedia.org/w

They are basically visualizations of the "integral curves" defined by the vector field. https://en.wikipedia.org/wiki/Integral_curve https://en.wikipedia.org/wiki/Integral_curve You can think of the vector field as the definition of a differential equation, i.e. it gives the rate of change of each coordinate at each point. The solution of the differential equation, given a start point, is then some curve, which is locally tangent to the vector field at every point. I think one is usually more interested in the solution curves than in the vector field itself, particularly in 3d. As the vector field itself would render as a cloud of little isolated lines which don't reveal much structure, whereas the solution curves show a lot of structure (for sufficiently dense lines, forming 3d structures like ribbons, sheets, helices, etc.). In 2d, one can get away with rendering little arrows and still produce a decent looking visualization, e.g. https://github.com/anvaka/fieldplay https://github.com/anvaka/fieldplay (which I would agree, is a genuine "vector field renderer").