This particular example is meant to depict the
electric field in a cyclotron, i.e. the electric
field induced by a magnetic field that is uniform
in space and steadily increasing as a function of
time.
Non-experts tend to think that everything that is
a function of position has to be a potential, but
it's just not true.
Pick two points A and B and count how many steps
you go down along a path from A to B. The answer
depends on your choice of path. For a potential,
the answer would be independent of path.
I'm moderately pleased with how this looks. This
is the tenth scheme I tried. The first nine looked
awful.
My next agenda item is to extend the technique to
handle cases where the magnitude (not just direction)
of the one-form depends strongly on position. This
is needed for e.g. thermodynamics, where PdV is an
important non-potential.