Mathermatical Portraits

invisible visibility / mathematical portraits

In the mid-1980s, the first scientific PHSColograms were created with Donna Cox and her team at NCSA, and visualized four-dimensional mathematical models of the Etruscan Venus. Additional PHSColograms were created with Dan Sandin and John Hart of fractals and strange attractors. These PHSColograms uniquely explored the beauty of mathematics as abstraction found in nature and in relation to ornamentation and architecture.

Selected works were shown by Hudson at Feature Inc. in Chicago, at Fermilab in 1987, and in the Science in Depth traveling exhibition, sponsored by ACM that premiered at the Museum of Science and Industry in Chicago, and toured to the Computer Museum Boston and NASA Ames Visitors Center, concluding at SIGGRAPH ’92 Chicago in which 40 PHSColograms were installed around the Electronic Visualization Lab’s VR CAVE debut.

Forms generated by elliptic ovals have fascinated geometers, artists, and astronomers ever since Appollonius, da Vinci, and Kepler. These “ovalesques" come from Topology and began their computer graphics existence on an Apple program in Forth.

-George FrancisNational Center for Supercomputing Applications,

University of Illinois at Urbana-Champaign

Fractal Forest

This is a forest that existed only inside of a computer. It is made out of highly detailed (fractal ) shapes that look like objects in the real world, such as trees and grass. The elm trees are trunks with smaller elm trees growing out of them. The branches of the pine trees are smaller pine trees themselves. Each blade of grass is actually a tiny field of grass—so tiny that you cannot see them here. These objects are constructed from smaller copies of themselves. This is called "self-similarity", and is the way most fractals are made.

Detail from John Hart's Fractal Forest animation shown at the SIGGRAPH '91 Electronic Theatre.

Fractal Forest, 1991

Ellen Sandor & (art)n: Stephan Meyers, Janine Fron and Craig Ahmer

John Hart

Virtual Photograph/PHSCologram: Cibachrome, Kodalth, Plexiglas

24 x 20 inches

Fourplay

A juxtaposition of four related fractals, each of which has a certain "four-ness" about it. The fractal in front is a "Quaternion Julia Set," and in back we see the "Mandelbrot Set" and the "Complex Subset Julia Set." A Julia Set is a sort of Strange Attractor. A Mandlebrot Set is an encyclopedia or map of all possible Julia Sets. This map is a fractal, and it may be the most complex shape in mathematics.

Fourplay, 1990

Ellen Sandor & (art)n: Stephan Meyers

John Hart

Virtual Photograph/PHSCologram: Cibachrome, Kodalith, Plexiglas

(24 x 20), (48 x 40) inches

See: Virtual Sculpture: Chaos/Information as Ornament: A Tribute to Louis Sullivan

Stacked Julia Set I

Stacked Julia Set I, 1989

Ellen Sandor & (art)n: Stephan Meyers

Dan Sandin, Electronic Visualization Lab, School of Art and Design, University of Illinois at Chicago

Virtual Photograph/PHSCologram: Cibachrome, Kodalith, Plexiglas

24 x 20 inches

See: Virtual Sculpture: Chaos/Information as Ornament: A Tribute to Louis Sullivan

Strange Attractor

Strange Attractor, 1989

Ellen Sandor & (art)n: Stephan Meyers

Dan Sandin, Electronic Visualization Lab, School of Art and Design, University of Illinois at Chicago

Virtual Photograph/PHSCologram: Cibachrome, Kodalith, Plexiglas

24 x 20 inches

See: Virtual Sculpture: Chaos/Information as Ornament: A Tribute to Louis Sullivan

Julius Loves Mary

Julius Loves Mary, 1988

Ellen Sandor & (art)n: Stephan Meyers

Mary Rasmussen
Dan Sandin, Electronic Visualization Lab, School of Art and Design, University of Illinois at Chicago

Virtual Photograph/PHSCologram: Kodalith, Kodalth, Plexiglas

14 x 11 inches

Fractal Pleasure

A virtual photograph of a fractal.

Fractal Pleasure, 1988

Ellen Sandor & (art)n: Stephan Meyers

Dan Sandin, Electronic Visualization Lab, School of Art and Design, University of Illinois at Chicago

Virtual Photograph/PHSCologram: Kodalith, Kodalth, Plexiglas

14 x 11 inches

STACKED JULIA SET II

Detail from Chaos/Information as Ornament:

A Tribute to Louis Sullivan and Dan Sandin's Stacked Julia Set animation shown at the SIGGRAPH '94 Electronic Theatre.

A progression of two-dimensional fractals stacked on top of one another like plates, forming a single three-dimensional fractal.

Stacked Julia Set II, 1990

Ellen Sandor & (art)n: Stephan Meyers

Dan Sandin and Tom DeFanti, Electronic Visualization Lab, University of Illinois at Chicago

Virtual Photograph/PHSCologram: Cibachrome, Kodalth, Plexiglas

24 x 20 inches

Eine Kliene Nachtlicht

The hilly ground and the pattern on the moon are both fractals, which make them look rough and natural. The name means "A Little Night Light" and is a pun on "Eine Kleine Nachtmuzik," a piece of music by Mozart.

Eine Kliene Nachtlicht, 1991

Ellen Sandor & (art)n: Stephan Meyers

F. Kenton Musgrave & Benoit Mandlebrot, Yale University

vintage PHSCologram: computer interleaved Crosfield Cibachrome and Kodalith films mounted on plexigla

20 x 24 inches

Extensions to the Twin Dragon

The wood floor is created of tiles with the shape of the "twin dragon," a two-dimensional fractal form. The cauliflower-like shape resting on the floor is a three-dimensional version of this same shape. It is constructed from an iterated function system, a mathematical technique which uses feedback to create a shape, something like pointing a videocamera at the monitor its image is displayed on.

Extensions to the Twin Dragon, 1990

Ellen Sandor & (art)n: Stephan Meyers

John Hart, Washington State University

Special thanks to Dan Sandin and Tom DeFanti, Electronic Visualization Lab, School of Art and Design, University of Illinois at Chicago

Vintage PHSCologram: computer interleaved Crosfield Cibachrome and Kodalith films mounted on plexiglas

24 x 20 inches

O'Keeffe III

"A flower is relatively small. Everyone has many associations with a flower-the idea of flowers. You put out your hand to touch the flower-lean forward to smell it-maybe touch it with your lips almost without thinking-or give it to someone to please them. Still-in a way-nobody sees a flower-really-it is so small-we haven't time-and to see takes time, like to have a friend takes time. If I could paint the flower exactly as I see it no one would see what I see because I would paint it small like the flower is small. So I said to myself-I'll paint what I see-what the flower is to me but I'll paint it big and they will be surprised into taking time to look at it-I will make even busy New Yorkers take time to see what I see of flowers.”

–Georgia O'Keeffe on White Rose III

A visualization of a mathematical formula juxtaposed with a scanned image of "White Rose III" 1927, (oil on canvas, 36x30) by Georgia O'Keeffe. This mathematical image is not a fractal.

O'Keeffe III , 1990

Ellen Sandor & (art)n: Stephan Meyers

Clifford Pickover, IBM

Vintage PHSCologram: computer interleaved Crosfield Cibachrome and Kodalith films mounted on plexiglas

24 x 20 inches

Rhomboy Homotopies

The first of the computer-generated PHSColograms was produced using the same camera as that used for the real-time objects, however, the image was photographed from a computer monitor. Between each of the nine exposures, the lens of the camera and the "stage" on which the monitor was placed were moved. The image on the monitor was also changed to simulate the perspective change with a real-time object. Because the only light entering the camera was the soft glow of the computer monitor, a special, very fast film had to be used.

Portraits of a Romboy Homotopy, a four dimensional mathematical object:

Lotus, Magritte, Ball of Fire, Apollo, Etruscan Venus, Cupid, Transparent Venus, Transparent Lotus and Transparent Apollo

Rhomboy Homotopies, 1986

Ellen Sandor & (art)n

Donna Cox, George Francis and Ray Idaszak, NCSA, University of Illinois at Urbana-Champaign
Tom DeFanti and Dan Sandin, Electronic Visualization Lab, School of Art and Design, University of Illinois at Chicago

Special thanks to Larry Smarr, NCSA, University of Illinois at Urbana-Champaign

Computer/Camera Technique PHSColograms: Chromalin, Kodalith, Plexiglas

(24 x 20), (14 x 11) inches