The Traveling CANVAS - CalculArt at Dennos
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Works by The illiMath Collective

Cubocta | Curved Minus 3 | Dirac Belt Trick | Etruscan Venus | Evert.Full | Eye.Full | illiSnail
Lorenz Strange Attractor | Minimax | Möbius | Rikitake | Quasi Crystals
works in situ

The illiMath Collective is a group of students, scholars, professors, artists, scientists, and others based at the University of Illinois at Urbana-Champaign and the University of Illinois at Chicago who have created mathematical artworks since the late 1980s.

The illiMath Collective includes:
Abby Watt, Alex Bourd, Ben Bernard, Ben Schaeffer, Bob Patterson, Camille Goudeseune, Carolina Cruz-Neira, Cary Sandvig, Charles Gunn, Chris Hartman, Chris Rainey, Dan Sandin, Dana Plepys, Donna Cox, Doug Nachand, Emily Echevarria, George Francis, Glenn Chappell, Hank Kaczmarski, Jeff Carpenter, Jeff Weeks, John Estabrook, John M Sullivan, Lou Kauffman, Matt Hall, MAtt Woodruff, Maxine Brown, Michael Pelsmajer, Mimi Tsuruga, Nicholas Duchnowski, Pat Hanrahan, Paul McCreary, Peter Brinkmann, Rachael Brady, Ray Idaszak, Rose Marshack, Steffen Weissmann, Stuary Levy, Tamara Munzer, Ted Emerson, Tom DeFanti, Tony Robbin, Ulises Cervantes, Ulrike Axen, and William Baker.

'Cubeocta' by The illiMath Collective

Cubocta


The illiMath Collective, 1992
immersive interactive environment

A cube with corners cut off becomes a cuboctahedron. This polyhedral sphere turns inside-out in a motion called an eversion.

Animation: Chris Hartman
Code: François Apéry
Mathematics: Bernard Morin
Modeler: Richard Denner
From "The Optiverse," Francis, Levy, Sullivan, 1998

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'Curved Minus 3' by The illiMath Collective

Curved Minus 3


The illiMath Collective, 1992-1998
immsersive interactive environment

Curved Minus 3 offers the chance to experience a world where the rules of geometry differ from the rules of Euclidean geometry which we experience everyday. This piece is an example of a hyperbolic space tiled by twelve-sided dodecahedra. Here the pentagonal surfaces of the dodecahedra have five 90° angles, an impossibility in the Euclidean world.

Animation: Chris Hartman, Paul Chappell
Geometry: Charles Gunn, Mark Phillips
Syzygy: Ben Bernard, Matt Woodruff, Ben Schaeffer

From "The Post-Euclidean Walkabout" SIGGRAPH 94

Download the Curved Minus 3 interactive computer application and Quicktime movie.

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'Dirac Belt Trick' by The illiMath Collective

Dirac Belt Trick


The illiMath Collective, 1993
immersive interactive environment

Dirac Belt Trick explores the rotation of objects connected by a belt or by strings to a fixed background. Such an object plus its connections to the background will be entangled by a 360° turn, yet returned fully to its original configuration after a 720° rotation. This combination of topology and geometry has applications to the physics of an electron.

Animation: Chris Hartman
Book: George Francis
Mathematics: Lou Kauffman
Production: Dan Sandin

From "Air on the Dirac Strings," SIGGRAPH 93

Download the Dirac Belt Trick interactive computer application and Quicktime movie.

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'Etruscan Venus' by The illiMath Collective

Etruscan Venus


The illiMath Collective, 1989
PHSCologram and immersive interactive application

In the 1980's, when 3D computer-generated mathematical visualizations were created, they were generally created on graphical supercomputers manufactured by Silicon Graphics, computers often residing at National Science Foundation-funded supercomputer centers across the country. Two such locations shared a common, but geographically-disparate university, the University of Illinois at Urbana-Champaign and Chicago. Professor Donna Cox, George Francis and Ray Idaszak at UIUC and Ellen Sandor, Tom DeFanti and Dan Sandin at UIC collaborated on a PHSCologram titled "Etruscan Venus." Described by the artists as "a video portrait of a Romboy Homotopy, a four dimensional object," the viewer is able to see three of those four dimensions without the aid of stereo glasses due to the partial masking of the multiple images by a lenticular film in front of each image. An additional "Venus" is available in the CANVAS, where the viewer can maneuver the image through various 3D slices of the 4D object.

Download the Etruscan Venus interactive computer application.

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'Evert.Full' by The illiMath Collective

Evert.Full


The illiMath Collective, original 1998, reproduced 2006
UltraChrome K3 on Piezo Pro Matte Canvas media
59.5 x 39.25 in.

The minimax sphere eversion from The Optiverse, a video by John M Sullivan, George Francis and Stuart Levy, with original music by Camille Goudeseune, produced at the Univeristy of Illinois (Mathematics Department and NCSA).

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'Eye.Full' by The illiMath Collective

Eye.Full


The illiMath Collective, original 1998, reproduced 2006
UltraChrome K3 on Piezo Pro Matte Canvas media
59.5 x 39.25 in.

An inside view of an everting sphere from The Optiverse, a video by John M Sullivan, George Francis and Stuart Levy, with original music by Camille Goudeseune, produced at the Univeristy of Illinois (Mathematics Department and NCSA).

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'illiSnail' by The illiMath Collective

illiSnail


The illiMath Collective, 1992-2008
immersive interactive environment

All the forms in illiSnail are projections of ruled, minimal surfaces in spherically curved space, where the rules of geometry differ from those of our flat, Euclidean space.

illiSnail morphs a Möbius band into such familiar shapes as Steiner crosscap, Roman surface, Clifford torus, Lawson bottle aka Brehm knotbox.

Download the illiSnail interactive computer application and Quicktime movie.

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'Lorenz Strange Attractor' by The illiMath Collective

Lorenz Strange Attractor


The illiMath Collective, 1998
immsersive interactive application

The Lorenz dynamical system illustrates two features of chaos: the butterfly effect and a strange attractor. All particles start from approximately the same initial position and, although governed by identical laws of motion, the particles soon disperse wildly. Eventually their paths converge and they are destined to wander back and forth on the attractor in an unpredictable way.

CANVAS Implementors:
Chris Rainey, REU Summer 2006
Kyle Wilkinson, Math 198, Spring 2006
Stan Blank's high school class, 2005

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'Minimax' by The illiMath Collective

Minimax


The illiMath Collective, 1998
immersive interactive application

Bernard Morin's central model is a strongly contorted sphere that penetrates itself with a bending energy of four spheres. The Minimax eversion turns a single sphere inside out by morphing it through the central model. To do this, a blue-green inside/red-orange outside sphere must contort into the central model by raising its energy before sliding down the other side of the energy saddle to change colors.

Geometry: Rob Kusner
Surface Evolver: Ken Brakke
Animation: Alex Bourd, Chris Hartman
Sound: Camille Goudeseune
Post-Production: Jeff Carpenter, Dana Plepys

From "The Optiverse," Francis, Levy, Sullivan, 1998

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'Mobius' by The illiMath Collective

Möbius


The illiMath Collective, 1998
immersive interactive environment

Bernard Morin's central model pirouettes in four space to show her best face for projection into three space where we can admire her shape. Despite appearances, the bending energy of the surface does not change during this inversion.

From "The Optiverse," Francis, Levy, Sullivan, 1998

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'Rikitake' by The illiMath Collective

Rikitake


The illiMath Collective, 2008
immersive interactive environment

Rikitake, like Lorenz Strange Attractor, illustrates a dynamical system where particles starting from almost the same point in space eventually follow their own separate, but never too separate, paths.

CANVAS Implementors:
Nicholas Duchnowski & Chris Rainey
Kyle Wilkinson, Math 198, Spring 2006
Stan Blank's high school class, 2005

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'Quasi Crystals' by The illiMath Collective

Quasi Crystals


The illiMath Collective, 2004-2007
immersive interactive environment

Quasi Crystals shows a small part of a space packing by non-rectangular bricks which lacks all symmetry. It is computed as a 3-dimensional shadow of a 6-dimensional cubical lattice. It is necessary to show the shadow rather than the 6D object because it is impossible to say what the hypercube looks like; as it would be impossible to describe a 3D cube to a being living in only two dimensions, it is impossible for humans (who perceive three dimensions) to visualize a 6D object.

Mathematics: DeBruijn, Gregory, Robbin.

More information on Quasi Crystals.

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