Dynamics of Mandelbrot set with Transcendental Function

Abstract

These days Mandelbrot set with transcendental function is an interesting area for mathematicians. New equations have been created for Mandelbrot set using trigonometric, logarithmic and exponential functions. Earlier, Ishikawa iteration has been applied to these equations and generate new fractals named as Relative Superior Mandelbrot Set with transcendental function. In this paper, the Mann iteration is being applied on Mandelbrot set with sine function i.e. sin(zn)+c and new fractals with the concept of Superior Transcendental Mandelbrot Set will be shown. Our goal is to focus on the less number of iterations which are required to obtain fixed point of function sin(zn)+c.