The Picard–Mann iteration with s-convexity in the generation of Mandelbrot and Julia sets
In recent years, researchers have studied the use of different iteration processes from fixed
point theory in the generation of complex fractals. For instance, the Mann, Ishikawa, Noor …
point theory in the generation of complex fractals. For instance, the Mann, Ishikawa, Noor …
Numeric characteristics of generalized M-set with its asymptote
The Mandelbrot set (M-set) formulated by fc (z)= z 2+ c is important in chaos theory. It has
been extended into generalized M set (kM set) fc (z)= z k+ c by using different exponent k …
been extended into generalized M set (kM set) fc (z)= z k+ c by using different exponent k …
Mandelbrot sets and Julia sets in Picard-Mann orbit
C Zou, AA Shahid, A Tassaddiq, A Khan… - IEEE Access, 2020 - ieeexplore.ieee.org
The purpose of this paper is to introduce the Mandelbrot and Julia sets by using Picard-
Mann iteration procedure. Escape criteria is established which plays an important role to …
Mann iteration procedure. Escape criteria is established which plays an important role to …
[PDF][PDF] Fractal generation method based on asymptote family of generalized Mandelbrot set and its application
Generalized Mandelbrot set (kM set) is the basis of fractal analysis. This paper presents a
novel method to generate kM set, which generates kM set precisely by constructing its …
novel method to generate kM set, which generates kM set precisely by constructing its …
The generalized M–J sets for bicomplex numbers
X Wang, W Song - Nonlinear Dynamics, 2013 - Springer
We explained the theory about bicomplex numbers, discussed the precondition of that
addition and multiplication are closed in bicomplex number mapping of constructing …
addition and multiplication are closed in bicomplex number mapping of constructing …
Fractal properties of the generalized Mandelbrot set with complex exponent
Mandelbrot set, which was provided as a highlight in fractal and chaos, is studied by many
researchers. With the extension of Mandelbrot set to generalized M set with different kinds of …
researchers. With the extension of Mandelbrot set to generalized M set with different kinds of …
Stability, data dependence, and convergence results with computational engendering of fractals via Jungck–DK iterative scheme
We have developed a Jungck version of the DK iterative scheme called the Jungck–DK
iterative scheme. Our analysis focuses on the convergence and stability of the Jungck–DK …
iterative scheme. Our analysis focuses on the convergence and stability of the Jungck–DK …
Escape criteria using hybrid Picard S-iteration leading to a comparative analysis of fractal Mandelbrot sets generated with S-iteration
R Srivastava, A Tassaddiq, RM Kasmani - Fractal and Fractional, 2024 - mdpi.com
Fractals are a common characteristic of many artificial and natural networks having
topological patterns of a self-similar nature. For example, the Mandelbrot set has been …
topological patterns of a self-similar nature. For example, the Mandelbrot set has been …
[图书][B] Fractal control and its applications
ST Liu, YP Zhang, CA Liu - 2020 - books.google.com
The book focuses on fractal control and applications in various fields. Fractal phenomena
occur in nonlinear models, and since the behaviors depicted by fractals need to be …
occur in nonlinear models, and since the behaviors depicted by fractals need to be …
Generalized fuzzy Mandelbrot and Mandelbar sets
In this article, we introduce the generalized fuzzy Mandelbrot and Mandelbar sets. In this
regard, we assign a membership value to each complex number under the iterations, even if …
regard, we assign a membership value to each complex number under the iterations, even if …