These are the critical sets of various charged knots. The electric potential at a point x is defined as the integral of the inverse distance from x to the knot, with respect to arc length. At each of the plotted points, the net electric force is zero. The points are colored by their electric potentials. The locus of all points equal to a critical point's potential will be a smooth surface with one or more singularities. For regular values, the locus will be a smooth surface, and you can view interactive plots of some of them here.

Left click and drag to rotate. You can toggle between rotating, panning, and zooming with the icons in the upper right. Use the drop down menu to choose between different knots. Visualized with Plotly.