This video was made to test out a relativistic version of Direct Coulomb Summation and is intended to be displaying fields of different moving charge configurations.
Coulomb’s Law is well defined and also that inverse square fields propagate at the speed of light is well known. Hence why not put both into the same equation.
In general, the video uses Coulomb's law to compute an observational cube of data. The dataset is then sent to a ray tracer which produces the images in the video. The background colors show the potential energy contours of different pole configurations. The colors red green blue are used in an alternating sequence for adjacent contours; highlighting the structure of the magnetic fields.
Using the same dataset, small streamline particles (white dots) were added to each frame showing the vector paths around the magnets, which is typically perpendicular to the potential energy contours.
The individual data points can be verified using a simple calculation known to first year physics students. The difference being that instead of one or two points, 33 million points were calculated and then visualized in a 3d space