This video was made to test the modeling of electric current with Direct Coulomb Summation on Nvidia GPU's. It is using 1.2 million dipole charges in stacked radial loops to model electric current. The simulations were computed on a GTX 560 over a few days.
In general, the video uses Coulomb's law to compute an large 321x321x321 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 are typically perpendicular to the potential energy contours. You can think of the white dots like a leaves on a river or snow flakes in a storm.
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 per video frame.