Due to the rotation of the Earth, over the course of the night, stars will appear to turn around the celestial pole. This means we can photograph star trails (desired or not). Physically, any star trail should form a great circle over the celestial sphere, and in most photographs of star trails, this is indeed the case:
Yet I have also seen photographs where star trails form a spiral or seem to be coming into or out of a line. There are several examples in this photographylife blog, including one where the stars appear as a complicated vector field, one where they make a full circle (which should be possible during 24 hours of clear weather poleward of 85° only, with a 24-hour exposure), and one where the star trails appear like half-parabolas eminating from a line. How can such images be created?