1. illiSnails
  2. Minimax triversion of the sphere
  3. illiPhaser

Conformal projections to Euclidean space of Blaine Lawson's ruled minimal surfaces in 3-dimensional spherical space realized with the real-time interactive CAVE animator ``illiSnail'' created by Glenn Chappell, Chris Hartman and George Francis of the NCSA 1994 illiView team.


Minimax triversion of the sphere, by George Francis, John Sullivan, Chris Hartman, and Stuart Levy of the NCSA/UIUC, Rob Kusner of UMass, Ken Brakke of Susquehanna University.

A sphere can be turned inside out without tearing if it is allowed to pass through itself; the sphere eversion shown here was computed automatically by starting with the halfway model (where the orange and blue sheets pass through each other) and simplifying it by numerically minimizing a surface bending energy.


[choose one of the three images below]

Trajectories in the May-Leonard dynamical system, a highly simplified model of populations of three competing species. It was generated by illiPhaser [http://www.ncsa.uiuc.edu/VR/cavernus/PHASER/Phaser.html], developed by Alex Bourd, George Francis, and Jonathan Manton of the illiView group at the NCSA, University of Illinois.

Note: the full-sized versions of the May-Leonard images below have been removed for lack of space -- if you need them, please write to slevy@ncsa.uiuc.edu.
Trajectories in the May-Leonard dynamical system. All images 3072x3980
[May-Leonard1.tiff] [May-Leonard2.tiff] [May-Leonard3.tiff]
http://www.ncsa.uiuc.edu/People/slevy/May-Leonard1.tiff http://www.ncsa.uiuc.edu/People/slevy/May-Leonard2.tiff http://www.ncsa.uiuc.edu/People/slevy/May-Leonard3.tiff

Stuart Levy, slevy@geom.umn.edu or slevy@ncsa.uiuc.edu