Last edited 7jun99 by gfrancis@uiuc.edu
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Math Gallery for the DMS Director at the NSF


Etruscan Venus: Red

(C)1989 Donna Cox, George Francis, Ray Idaszak, NCSA.

http://new.math.uiuc.edu/venus

This surface is a Whitney-stable 3D projection of a nonorientable surface with Euler characteristic 0 (a Kleinbottle) embedded in 4-space. Like Steiner's ``Roman Surface'', the ``Etruscan Venus'' loses its singularities under Fran\c cois Ap\' ery's ``Romboy'' homotopy and becomes an immersed surface equivalent to the connected sum of two copies of ``Boy's Surface.''

G.Francis, {\sc The Etruscan Venus}. In P. Concus, R. Finn, D. Hoffman (Eds.) {\it Geometric Analysis and Computer Graphics.} Mathematical Sciences Research Institute Publications. Springer-Verlag, N.Y. 1991.

Optiverse: ICM98 Berlin Poster

(C)1998 George Francis, John Sullivan, Stuart Levy

http://new.math.uiuc.edu/optiverse

This image graced the main poster of the International Congress of Mathematicians in Berlin, August 1999. It is a detail of the four "isthmus events" that open/close the ears of Morin's Surface during the eversion of a sphere.

Weaire-Phelan Foam: Relaxed Voronoi Cells

(C) 1999 John Sullivan, Stuart Levy

http://www.math.uiuc.edu/ ~jms

The Weaire-Phelan foam is a counterexample to Kelvin's conjecture about the best partition of space into equal-volume cells.

Computer graphic by John M. Sullivan, Math. Dept., Univ. of Illinois.

See http://www.math.uiuc.edu/~jms/ for more information.

Optiverse: Minimax Sphere Eversion

(C)1998 John Sullivan, George Francis, Stuart Levy

http://new.math.uiuc.edu/optiverse

The principal stages of this Morin eversion are arranged about the border of this composite.

With the assistance of Camille Goudeseune, the image was raytraced with Renderman on a Silicon Graphics Onyx 2 in the Numerical Laboratory of the National Center for Supercomputing Applications and the VisLab of the Beckman Institute at the University of Illinois at Urbana-Champaign.

This Irisprint was made from its electronic database by Digicolor.

Optiverse: Framework Interior

(C)1998 John Sullivan, George Francis, Stuart Levy

http://new.math.uiuc.edu/optiverse

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Eggmath Poster

(C) 1999 Steven Bradlow, John Sullivan, Janet Hanlon

http://new.math.uiuc.edu/ eggmath

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illiSnail: Lawson's Minimal Surfaces

(C)1997 George Francis, Chris Hartman, Glenn Chappell, Stuart Levy

http://new.math.uiuc.edu/snail

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illiPhaser: May-Leonard Dynamical System

(C)1997 George Francis, Alexei Bourd, Jonathan Manton, Stuart Levy

http://new.math.uiuc.edu/ phaser

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Optiverse: Triversion

(C)1998 John Sullivan, George Francis, Stuart Levy

http://new.math.uiuc.edu/optiverse

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http://new.math.uiuc.edu/WHO/

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Dodecaplex

John M. Sullivan

http://new.math.uiuc.edu/~jms/

This image of the dodecaplex graces the August `99 (SIGGRAPH) issue of CACM.