Boundaries of Filled Julia Sets in Generalized Jungck Mann Orbit

In this paper, we study the generalized Jungck Mann orbit (GJMO) and prove the converse theorem of results. We develop algorithms for the generation of filled Julia sets and their boundaries in the GJMO. In simple Julia set (i.e., boundary of filled Julia set), we show the internal structure of Julia set and establish the correspondence between Julia points via dark blue lines in graphs. Moreover, we demonstrate the pictorial effects of filled Julia set and its boundary and graphically present the image change with the change of complex parameter <inline-formula> <tex-math notation="LaTeX">$c$ </tex-math></inline-formula> in the GJMO.

[1]  Mamta Rani,et al.  Superior Mandelbrot Set , 2004 .

[2]  Shin Min Kang,et al.  Fixed point results in the generation of Julia and Mandelbrot sets , 2015 .

[3]  Nawab Hussain,et al.  On Rate of Convergence of Jungck-Type Iterative Schemes , 2013 .

[4]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[5]  Vasileios Drakopoulos,et al.  An overview of parallel visualisation methods for Mandelbrot and Julia sets , 2003, Comput. Graph..

[6]  Shin Min Kang,et al.  Mandelbrot and Julia Sets via Jungck–CR Iteration With $s$ –Convexity , 2019, IEEE Access.

[7]  M. Rani,et al.  Superior Julia Set , 2004 .

[8]  Mamta Rani,et al.  Effect of Stochastic Noise on Superior Julia Sets , 2009, Journal of Mathematical Imaging and Vision.

[9]  Renu Chugh,et al.  NEW JULIA AND MANDELBROT SETS FOR A NEW FASTER ITERATIVE PROCESS , 2016 .

[10]  Robert L. Devaney,et al.  A First Course In Chaotic Dynamical Systems: Theory And Experiment , 1993 .

[11]  Rudan Xu,et al.  An Image Encryption Algorithm Utilizing Julia Sets and Hilbert Curves , 2014, PloS one.

[12]  Shin Min Kang,et al.  Tricorns and Multicorns of -Iteration Scheme , 2015 .

[13]  Theodore Kim,et al.  Quaternion Julia Set Shape Optimization , 2015, SGP '15.

[14]  Shin Min Kang,et al.  Fractal Generation in Modified Jungck–S Orbit , 2019, IEEE Access.

[15]  Renu Chugh,et al.  Julia sets and Mandelbrot sets in Noor orbit , 2014, Appl. Math. Comput..

[16]  Guangxing Wang,et al.  COMPOSED ACCELERATED ESCAPE TIME ALGORITHM TO CONSTRUCT THE GENERAL MANDELBROT SETS , 2001 .

[17]  Robert L. Devaney,et al.  A Generalized Version of the McMullen Domain , 2008, Int. J. Bifurc. Chaos.

[18]  Krzysztof Gdawiec,et al.  Fixed point results for the complex fractal generation in the S -iteration orbit with s -convexity , 2018 .