The Art in Polynomiography of Special Polynomials

Bahman Kalantari
Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings (2003)
Pages 173–180


Polynomiography is the art and science of visualization in approximation of zeros of complex polynomials. It allows one to obtain many colorful images of polynomials. These images can subsequently be re-colored in many ways to create artwork. Polynomiography has tremendous applications in the visual arts, education, and science. Artistically, it can be used to create diverse set of beautiful images reminiscent of the intricate designs and modern art. Educationally, polynomiography can be used to teach mathematical concepts. Scientifically, it provides a tool, not only for viewing polynomials, present in virtually every branch of science, but also a tool to discover new theorems. The goal of this paper is to present some artwork produced via polynomiography of a few polynomials arising in science as well as a few considered to arrive at beautiful but. anticipated designs. These include a Chebyshev polynomial, a polynomial arising in physics, one in knot theory, and some based on roots of unity. The purpose of the paper is doing art on these special polynomials. But the reader will realize that these images also help engrave certain attributes of these polynomials. Moreover the beauty of these images suggests an infinite jewel box of polynomials yet to be discovered and visualized through polynomiography by future polynomiographers. The ultimate goal here is to suggest that polynomiography is indeed a new art form that can be thought of as "painting by numbers" or "painting by points." In a sense it is one of the most minimalistic art forms.