Knot Energies in 3-space:

Here are some graphics for a knot with various knot energies (this particular knot is a 15 crossing knot suggested by Morwen Thisthlethwaite, will need to look up and see exactly which one):

Above is a knot with six energies (different powers of the usual knot energy)

In order of increasing power: dark blue, light blue, green, yellow, orange, red.

Above is same knot (different viewpoint, with three energies (different powers of the usual knot energy)

In order of increasing power: blue, white, red.

Here is the same knot as a knotted arc ( in minimal energy configuration.