The second example is a program I have used for many years as a benchmark for testing hardware and software. It plots orbital motion in central-force fields that vary as a power of the distance from the force center. One can choose from three different powers: direct first power (the spring), inverse second power (gravity), and inverse first power. The spring and gravity orbits close, and the parameters are chosen to make the inverse first power orbit appear to close (it makes a pretty picture).