Shin Min Kang - Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea. Shahid M. Ramay - College of Science, Physics and Astronomy Department, King Saud University, Riyadh, Saudi Arabia. Muhmmad Tanveer - Department of Mathematics and Statistics, University of Lahore, Lahore 54000, Pakistan. Waqas Nazeer - Division of Science and Technology, University of Education, Lahore 54000, Pakistan.
The aim of this paper is to present some artwork produced via polynomiography of a few complex polynomials and a few special polynomials arising in science as well as a few considered to arrive at beautiful but anticipated designs. In this paper an iterative method corresponding to Simpson's \(\frac{1}{3}\) rule is used instead of Newton's method. The word ''polynomiography'' coined by Kalantari for that visualization process. The images obtained are called polynomiographs. Polynomiographs have importance for both the art and science aspects. By using an iterative method corresponding to Simpson's \(\frac{1}{3}\) rule, we obtain quite new nicely looking polynomiographs that are different from Newton's method. Presented examples show that we obtain very interesting patterns for complex polynomial equations, permutation matrices, doubly stochastic matrices, Chebyshev polynomial, polynomial arising in physics and Alexander polynomial in knot theory. We believe that the results of this paper enrich the functionality of the existing polynomiography software.
Shin Min Kang, Shahid M. Ramay, Muhmmad Tanveer, Waqas Nazeer, Polynomiography via an iterative method corresponding to Simpsons \(\frac{1}{3}\) rule, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 967--976
Kang Shin Min, Ramay Shahid M., Tanveer Muhmmad, Nazeer Waqas, Polynomiography via an iterative method corresponding to Simpsons \(\frac{1}{3}\) rule. J. Nonlinear Sci. Appl. (2016); 9(3):967--976
Kang, Shin Min, Ramay, Shahid M., Tanveer, Muhmmad, Nazeer, Waqas. "Polynomiography via an iterative method corresponding to Simpsons \(\frac{1}{3}\) rule." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 967--976
