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.
Highlights
Complex dynamics have a new significant development with the explosion of popular interest in the beautiful fractal objects that form the subject matter of the theory [5,6]
Authors found the region M of nonescape corresponds to a principal central bulb set with a fractal series of black hearts, including a series lining the x-axis, and that any c value in M corresponds precisely to Julia set kernels of the corresponding quadratic type [7]
Definition (Superior Julia sets) The set of complex points SK whose orbits are bounded under superior iteration of a function Q is called the filled superior Julia set
Summary
Complex dynamics have a new significant development with the explosion of popular interest in the beautiful fractal objects that form the subject matter of the theory [5,6]. There are similarities between magnified positions of the Mandelbrot set and the corresponding filled Julia set holds only near certain c values such as the central junctions of the antenna These are c values, for which 0 is eventually periodic; such c values are called Misiurcwicz points [10]. B. Definition (Superior Orbit) The sequences xn constructed above is called Mann sequence of iteration or superior sequences of iterates. Definition (Superior Orbit) The sequences xn constructed above is called Mann sequence of iteration or superior sequences of iterates We denote it by SO(x0, s, t) [11,12]. C. Definition (Superior Julia sets) The set of complex points SK whose orbits are bounded under superior iteration of a function Q is called the filled superior Julia set. If |F’(x0)|=1, the fixed point is neutral [10]
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