George K. Francis

The relationship between art and mathematics is a long one, joined by overlapping elements like scale and perspective and form that were recognized by both artists and mathematicians at least as far back as the Renaissance.

Today, the advent of powerful, advanced computer graphics is making the connections between math and art more intriguing than ever before and, quite naturally, a longtime Beckman Institute researcher occupies a unique place in the middle of that nexus. George Francis was putting abstract concepts into tangible form long before the computer age, but his vocation (mathematics professor) and avocation (art) became truly intertwined when computer advances enabled the development of mathematical visualization in the 1980s. Francis began using computers in the late 80s, about the same time his book featuring his mathematical drawings called A Topological Picturebook was published.

"I have always drawn pictures, all my life," Francis said. "That (book) is where I figured out how to draw mathematical pictures by hand. I actually started on the computer at about the same time. I'm still learning stuff about the computer."

Paralleling Francis' computer knowledge growth has been the development of highly advanced computer graphics and high-end venues utilizing those graphics like Beckman's six-sided immersive virtual reality environment, the Cube. Francis has been both a participant and a pioneer in this burgeoning world of enhanced graphics displays. He has been an adviser to students developing new technology in the field and to creators of virtual reality environments. He is also a leader in a campus initiative aimed at bringing the arts and technology together.

Francis is a Professor in the Department of Mathematics at the University of Illinois in the areas of geometry and topology and a member of the Beckman Institute's Image Formation and Processing group. He has been at Beckman from the beginning, working with the National Center for Supercomputing Applications (NCSA) when that unit was here and later with the Integrated Systems Laboratory (ISL) which operates the Institute's immersive virtual environments (IVEs) like the Cube and the CAVE™.

In addition to teaching subjects such as Hypergraphics and Advanced Aspects of Euclidean Geometry, Francis has been or is currently involved in numerous projects with his students and collaborators, including developing mathematical graphics programs for use by scientific researchers and by artists.

All of Francis' work revolves around mathematical visualization, a field of mathematics that has gained acceptance only fairly recently. In 1995 he co-authored a paper that he said sums up his ideas on geometry and graphics: "Mathematical visualization is the art of creating a tangible experience with abstract mathematical objects and concepts. While this process has been a cornerstone of the mathematical reasoning process since the times of the ancient geometers, the advent of high-performance interactive computer graphics systems has opened a new era whose ultimate significance can only be imagined."

Now, that significance is being realized in three ways, Francis said.

"The virtual environments (is one way)," he said. "The other thing that has been realized is that on your desktop you now have the power of a supercomputer."

The third thing is that the cost of doing high-end graphics work is coming down and the computing tools required to do that type of work are becoming more accessible. Francis said he is working with ISL on ways to make high end graphics systems like the Cube available to more users, especially artists.

Francis is one of the principal investigators on a proposal called VITA, short for Visual Information Technology for the Arts. The proposal includes a host of present and future projects revolving around using large-scale, interactive, immersive visualization and sonification displays that have proved their worth in scientific research for projects in the arts and humanities.