"The Optiverse" and Other Sphere Eversions

John M. Sullivan
Bridges: Mathematical Connections in Art, Music, and Science (1999)
Pages 265–274


For decades, the sphere eversion has been a classic subject for mathematical visualization. The 1998 video "The Optiverse" shows geometrically optimal eversions created by minimizing elastic bending energy. We contrast these minimax eversions with earlier ones, including those by Morin, Phillips, Max, and Thurston. The minimax eversions were automatically generated by flowing downhill in energy using Brakke's Evolver.