It's mostly an old demoscene effect, with tables for polar angle and distance. If you'd like to see the effect done much better, but without gameplay, the very direct inspiration was in "Gejmbåj." This was made in about five weeks before the deadline, and finished in complete panic on the final day. A lot of time in the middle was spent trying to distort a curve, with bizarre results, eventually leading to this simplified approach.
And about a week later my brain goes, "you know you could have just rotated a static image with affine sampling." If you'd like to see that effect pulled off gorgeously, check out the C64 demo "Mathematica." Execution is everything.