Results 1 to 10 of about 1,496 (159)
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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Review of "Fractals and Chaos: The Mandelbrot Set and Beyond", by B. Mandelbrot [PDF]
BioMedical Engineering OnLine, 2005 Diaspro Alberto
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Fuzzy Sets and Systems, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sóley Ersoy
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Visualization of Mandelbrot and Julia Sets of Möbius Transformations
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.
Darin Ulness, Leah Mork
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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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Fractal and FractionalThis 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, Danca Marius-F
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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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Generalized Mandelbrot Sets of a Family of Polynomials Pnz=zn+z+c;n≥2
International Journal of Mathematics and Mathematical Sciences, 2022 In this paper, we study the general Mandelbrot set of the family of polynomials Pnz=zn+z+c;n≥2, denoted by GM(Pn). We construct the general Mandelbrot set for these polynomials by the escaping method.
Salma M. Farris
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Shrubs in the Mandelbrot Set Ordering [PDF]
International Journal of Bifurcation and Chaos, 2003 We introduce shrubs in this paper in order to present a first approach to studying the structure of the Mandelbrot set. Primary, secondary… and N-ary shrubs are analyzed. We have experimentally obtained formulae to calculate the periods of the hyperbolic component representatives of the structural branches, and the preperiods and periods of both the ...
M. Romera +3 more
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Computational Geometry of Period-3 Hyperbolic Components in the Mandelbrot Set
Mathematics, 2021 A parametric theoretical boundary equation of a period-3 hyperbolic component in the Mandelbrot set is established from a perspective of Euclidean plane geometry.
Young-Hee Geum, Young-Ik Kim
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