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.