"The Optiverse" and Other Sphere Eversions

John M. Sullivan

Dept. of Mathematics, Univ. of Illinois, Urbana

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

This paper, "The Optiverse" and Other Sphere Eversions, is available here in HTML in two versions:

(The color version was formatted by Slavik Jablan for his online journal VisMath, which is available from the US or from Yugoslavia.)

A printable version (typeset in LaTeX) is available (in many formats) as ArXiv e-print math.GT/9905020.

An updated LaTeX version (with a few minor corrections) was prepared for publication by Springer in the proceedings of the Sep'00 Maubeuge Colloquium on Math and Art. It is now available here as a PDF file. This version has the highest-resolution images. The book Mathematics and Art: Mathematical Visualization in Art and Education, edited by Claude P. Bruter, will be published in June 2002.

This paper was first published in the proceedings of two summer 1999 conferences on mathematics and art: