The particles are attracted by the position of the mouse, each having a slightly different (randomized) attraction factor.

If a particle ever reaches the exact mouse coordinates, its position is randomly generated anywhere on the screen.

When rendering the particles, it simply draws a line between the previous and the new position. So when a particle is transported to a random place, it create the rays that appear around the cursor.

There's no real complexity in the maths involved, but I remember spending quite some time tweaking the random ranges to get something nice.