Daniel J. Sandin (computer artist) & Louis H. Kauffman (mathematician)

Caption: Looking east on the equator. (A frame from the computer animation "A Volume of Julia Sets," shown as a stereo 35mm Movie at Siggraph Electronic Theater in 1991.)

Title of Presentation:
Explorations & Visualizations of Higher Dimensional Julia Sets

Description of Project:
The Electronic Visualization Laboratory (EVL) is a shared facility of the School of Art and Design and the Computer Science Department at the University of Illinois at Chicago. EVL has been combining art and science for almost 30 years. It supports itself by supplying domain scientists with scientific visualizations, visualization techniques, advanced display technology and collaborative networked systems. The involvement of artists in the scientific research process has been central to EVL's success. Artists bring media expertise and visual communication knowledge to support communication between scientists and help scientists get insight from their data.

In this presentation we will outline a series of collaborative efforts between mathematician Louis Kauffman and media artist and technologist Dan Sandin.This collaboration started in the early 80s with renderings of two-dimensional Julia sets on pre-IBM PC computers such as the TRS 80 laptop and the Datamax UV1 (Z-BOX).

Julia sets and other fractals can exist in three and higher dimensions. We have been interested in visualizing these three-dimensional fractals both to understand their behavior and produce interesting images and animation.
The rendering of higher dimensional fractals is not trivial. Almost all of computer graphics is based on lighting and rendering polygons that represent the surfaces of objects. Since fractals are infinitely crinkly it's not clear how one would create a polygonal representation. Secondly, the lighting of polygons is based on determining a normal vector that represents the orientation of the polygon.

Since fractals are infinitely crinkly they don't have normals. Further, Julia sets are usually computed in two dimensions by iterating a function hundreds or thousands of times for each pixel. When this concept is extended to three dimensions the number of voxels (3-D pixels) becomes very large. In 1989 John Hart, a master of science graduate student in the computer science department at UIC, hit upon the idea of using a distance estimation technique witch made computation more efficient and provided a basis for determining surface orientation of three and higher dimensional fractal objects. A proof existed for a two-dimensional distance estimation technique and the form of the equations could be extended to higher dimensions. A proof of the three-dimensional distance estimation formulas eluded us until Yumei Dang, a student of Lou Kauffman pursuing a joint Ph.D. in mathematics and computer science, proved the distance estimation formulas to be correct. From this work two animations were produced; a one-minute 35mm stereo movie, "A Volume of Two-Dimensional Julia Sets" for Siggraph 1990 and a super high definition (2Kx2Kx60Hzへるつ) visualization of quaternion (4D) Julia sets for Nippon Telephone and Telegraph's 50th birthday celebration. This collaboration proved useful to the collaborators in several important ways. This collaboration has produced a series of artworks, new computer graphics rendering techniques, and mathematical proofs. In addition it was an excellent test vehicle for evaluating advanced computational and network techniques.

Our most recent project is a book "Hypercomplex Iteration, Distance Estimation and Higher Dimensional Fractals" with accompanying CD-ROM codifying and summarizing our fractal research.

Website Address for Documentation Materials: http://www.evl.uic.edu/hypercomplex/


Daniel J. Sandin is an internationally recognized pioneer of electronic art and visualization. He is director of EVL and an emeritus professor in the School of Art and Design at the University of Illinois at Chicago. As an artist, he has exhibited worldwide, and has received grants in support of his work from the Rockefeller Foundation, the Guggenheim Foundation, the National Science Foundation and the National Endowment for the Arts. In 1969, Sandin developed a computer-controlled light and sound environment called "Glow Flow" at the Smithsonian Institution and was invited to join the art faculty at the University of Illinois the same year. By 1973, he had developed the Sandin Image Processor, a highly-programmable analog computer for processing video images in real time. He then worked with DeFanti to combine the Image Processor with real-time computer graphics and performed visual concerts, the Electronic Visualization Events, with synthesized musical accompaniment. In 1991, Sandin and DeFanti conceived and developed, in collaboration with graduate students, the CAVE virtual reality (VR) theater. In recent years, Sandin has been concentrating on perfecting the design of the CAVE and its derivatives, the ImmersaDesk and the Infinity Wall. He presently is focused on the creation of art works in the VR medium with involve both video cameral materials and mathematical systems.

E-mail address: dan@uic.edu
Address: Daniel J. Sandin, Director, Electronic Visualization Laboratory (M/C 154), The University of Illinois at Chicago, 851 S. Morgan St. Rm 1120 SEO, Chicago IL 60607-7053, USA
Website address: www.evl.uic.edu/dan

Louis H. Kauffman
Born: February 3, 1945
High School: Norwood Norfolk Central High School (valedictorian 1962).
College: B.S. MIT, 1966.
Graduate School: PhD Mathematics, Princeton University, 1972.
Kauffman's research interests are in topology, knot theory in particular and in many fields that are related to these central interests. These fields include representation and exploration of topology, fractals and recursions using computers, logical and diagrammatic algebras, Hopf algebras, relations of topology with statistical mechanics and quantum field theory, foundations of discrete physics, quantum computing.

E-mail address: kauffman@uic.edu
Address: Math UIC, 851 South Morgan Street, Chicago, Illinois 60607-7045, USA
website address: http://www.math.uic.edu/~kauffman

BACK to >>> Sunday Schedule