Another Demonstration of mine was published at the Wolfram Demonstration Project. It helps to explore and create spherical artistic designs. I  generalized Lissajous curves to spherical coordinates. Azimuthal and polar angles undergo oscillations while the radius is kept constant. Although with the parameterization given I sought to emphasize the artistic side of Lissajous patterns, other spherical parameterizations were suggested for practical applications in MRI imaging. For details see M. Ullisch, T. Stöcker, M. Elliott, K. Vahedipour, and N. Shah, “Rigid Body Motion Detection with Lissajous Navigator Echoes,” Proceedings 17th Scientific Meeting, International Society for Magnetic Resonance in Medicine, 2009 p. 4650. The source code and interactive CDF written in app Mathematica producing these images can be found at the  Wolfram Demonstration Project.

Lissajous Patterns on a Sphere Surface