Mandelbrot Set as a Particular Julia Set of Fractional Order, Equipotential Lines and External Rays of Mandelbrot and Julia Sets of Fractional Order [PDF]
Fractal and Fractional, 2023 This paper deepens some results on a Mandelbrot set and Julia sets of Caputo’s fractional order. It is shown analytically and computationally that the classical Mandelbrot set of integer order is a particular case of Julia sets of Caputo-like fractional ...
Marius-F. Danca
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A strong construction of S-box using Mandelbrot set an image encryption scheme [PDF]
PeerJ Computer Science, 2022 The substitution box (S-box) plays a vital role in creating confusion during the encryption process of digital data. The quality of encryption schemes depends upon the S-box.
Mazzamal Aslam +6 more
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Significant Curves of the Mandelbrot Set
Mendel, 2021 The paper provides a description of some interesant curves contained in the Mandelbrot set. These curves are the boundaries of the areas called „bulbs“ which are described approximately only in present.
Dalibor Martisek
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The Mandelbrot set is the shadow of a Julia set [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2020 Working within the polynomial quadratic family, we introduce a new point of view on bifurcations which naturally allows to see the seat of bifurcations as the projection of a Julia set of a complex dynamical system in dimension three.
François Berteloot, Tien‐Cuong Dinh
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Mandelbrot Sets and Julia Sets in Picard-Mann Orbit
IEEE Access, 2020 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 generate Mandelbrot and Julia sets.
Cui Zou +4 more
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Visualization of Mandelbrot and Julia Sets of Möbius Transformations [PDF]
Fractal and Fractional, 2021 This work reports on a study of the Mandelbrot set and Julia set for a generalization of the well-explored function η(z)=z2+λ. The generalization consists of composing with a fixed Möbius transformation at each iteration step.
Leah K. Mork, Darin J. Ulness
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On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals. [PDF]
PLoS ONEOur study presents a novel orbit with s-convexity, for illustration of the behavior shift in the fractals. We provide a theorem to demonstrate the escape criterion for transcendental cosine functions of the type Tα,β(u) = cos(um)+αu + β, for [Formula ...
Khairul Habib Alam +4 more
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Anti Mandelbrot Sets via Jungck-M Iteration [PDF]
IEEE Access, 2020 Complex fractals achieved the highest popularity in the last ten years. Researchers used the fixed point iterations to visualize the fractals and compared the image generation times to check the efficiencies of iterations.
Hengxiao Qi +3 more
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MPI vs OpenMP: A case study on parallel generation of Mandelbrot set
Innovación y Software, 2020 Nowadays, some of the most popular tools for parallel programming are Message Passing Interface and Open Multi-Processing. It is of interest to compare these tools in solving the same kind of problems, because of the use of different ...
Ernesto Soto Gómez
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Escape Criteria Using Hybrid Picard S-Iteration Leading to a Comparative Analysis of Fractal Mandelbrot Sets Generated with S-Iteration [PDF]
Fractal and FractionalFractals 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 investigated and extended in several ways since it was first introduced, whereas ...
Rekha Srivastava +2 more
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