KALANTARI Bahman

Mathematician

Bahman Kalantari is an Associate Professor of computer science at Rutgers University. He holds a Ph.D. in computer science, an M.S. in mathematics, an M.S. in operations research and a B.S. in mathematics and physics. He has published over fifty articles in scientific journals on theoretical computer science, mathematics, operations research, as well as art-science journals and conference proceedings. His research interests include mathematical programming, linear programming, quadratic programming, convex programming, self-concordance theory, combinatorial and discrete optimization, linear algebra, nonnegative matrices, matrix scaling, matrix balancing, homogeneous programming, path-following and projective methods, duality theory, semi definite programming, global optimization, complexity of algorithms, approximation algorithms, approximation schemes, matching problems, traveling salesman problems, computational geometry, polynomial root-finding methods, iteration functions, approximation of functions, approximation of pi and techniques for the visualization of polynomial root-finding which he calls polynomiography, an interdisciplinary field with numerous applications in art, science, and education.

My images are created via a technique I have named polynomiography, a bridge between the Fundamental Theorem of Algebra and art. Polynomiography combines human creativity and computer power to create artwork of great variety and diversity. It provides a tool for artists to create a 2D image – a polynomiograph –  based on the computer visualization of a polynomial equation. The image is dependent upon the solutions of a polynomial equation, various interactive coloring schemes driven by iteration functions, and several other parameters under the control of the polynomiographer's choice and creativity. Polynomiography software can mask all of the underlying mathematics, offering a tool that, though easy to use, affords the polynomiographer infinite artistic capabilities, including images that are reminiscent of abstract art and the most sophisticated human designs.

A polynomial equation can be viewed as an algebraic description of a finite set of points in a plane. In this sense, polynomiography can be considered as painting via points, an art form capable of creating an interesting variety of images even by manipulating a small set of points, whether given explicitly, generated by a polynomial equation, or selected with the click of a mouse.

Polynomiography is somewhat analogous to photography where there are three main components: the photographer, the camera, and the subject. In polynomiography, there are also three main components: the polynomiographer, the computer software, that generates the polynomiographs, and the underlying polynomial equation. The final polynomiograph is produced by a combination of these three components. As in photography or in painting, polynomiography allows a great deal of creativity and choice.

There are several different techniques for producing polynomiographs. Generally speaking there is meaning and human control behind the images, as opposed to unpredictable or random computer-generated images that may only look interesting. The discovery of some of the images reminds me of Michelangelo's saying which is something like, "the sculpture is in the rock and all one needs to do is carve it out." There is an infinite source of beauty hidden behind the visualization of polynomial equations. All one needs to do is to discover these.

More information on polynomiography at: www.polynomiography.com.