We investigate in this paper the dynamics and the method of generating fractal images for Ishikawa iteration procedure. The geometry of relative superior Julia sets are explored for Ishikawa iteration.
We explore in this paper the dynamics of the complex function for non integer values, using the Ishikawa iterates. The z plane fractal images are studied for positive powers of the complex function while c plane fractals are analyzed for negative powers of the complex function.
We introduce in this paper the dynamics of Relative Superior Mandel-bar sets of inverse complex function for Ishikawa iteration. The z plane fractal images generated from the generalized transformation
The Binet formula for Pell sequence is viewed as a function of complex variable. In this paper the study of attracting and repelling fixed points of Pell sequence is presented with the complex dynamics resulting in the escape time images. A study of orbits of the Binet type formula is presented in the paper. Besides this, a new class of Mandelbrot sets is also studied for the Mann-iterates.
Complex graphics of dynamical system have been a subject of intense research nowadays. The fractal geometry is the base of these beautiful graphical images. Many researchers and authors have worked to study the complex nature of the two most popular sets in fractal geometry, the Julia set and the Mandelbrot set, and proposed their work in various forms using existing tools and techniques. Still researches are being conducted to study and reveal the new concepts unexplored in the complexities of these two most popular sets of fractal geometry. Recently, Ashish Negi, Rajeshri Rana and Yashwant S. Chauhan are among those researchers who have contributed a lot in the area of Fractal Geometry applications. In this paper we review the recently done work on complex and inverse complex functions for producing beautiful fractal graphics. The reviewed work mainly emphasizes on the study of the nature of complex and inverse complex functional dynamics using Ishikawa iterates and existence of relative superior Mandel-bar set.
The generation of fractals and study of the dynamics of polynomials is one of the emerging and interesting field of research nowadays. We introduce in this paper the dynamics of polynomials z n -z + c = 0 for n 2 and applied Jungck Ishikawa Iteration to generate new Relative Superior Mandelbrot sets and Relative Superior Julia sets. In order to solve this function by Jungck -type iterative schemes, we write it in the form of Sz = Tz, where the function T, S are defined as Tz = z n + c and Sz = z.Only mathematical explanations are derived by applying Jungck Ishikawa Iteration for polynomials in the literature but in this paper we have generated Relative Mandelbrot sets and Relative Julia sets.
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