Results 21 to 30 of about 1,561 (174)
A Four Step Feedback Iteration and Its Applications in Fractals
Fractal and Fractional, 2022 Fractals play a vital role in modeling the natural environment. The present aim is to investigate the escape criterion to generate specific fractals such as Julia sets, Mandelbrot sets and Multi-corns via F-iteration using complex functions h(z)=zn+c, h ...
Asifa Tassaddiq +4 more
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Relationship between the Mandelbrot Algorithm and the Platonic Solids
Mathematics, 2022 This paper focuses on the dynamics of the eight tridimensional principal slices of the tricomplex Mandelbrot set: the Tetrabrot, the Arrowheadbrot, the Mousebrot, the Turtlebrot, the Hourglassbrot, the Metabrot, the Airbrot (octahedron), and the Firebrot
André Vallières, Dominic Rochon
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Possibilities of Use for Fractal Techniques as Parameters of Graphic Analysis
Fractal and Fractional, 2022 Image processing remains an area that has impact on the software industry and is a field that is permanently developing in both IT and industrial contexts. Nowadays, the demand for fast computing times is becoming increasingly difficult to fulfill in the
Bogdan Popa +2 more
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The Mandelbrot set is the shadow of a Julia set
Discrete and Continuous Dynamical Systems, 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. We expect our approach to be extendable to other holomorphic families of dynamical systems.
Berteloot, François, Dinh, Tien-Cuong
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Operating with External Arguments of Douady and Hubbard
Discrete Dynamics in Nature and Society, 2007 The external arguments of the external rays theory of Douady and Hubbard is a valuable tool in order to analyze the Mandelbrot set, a typical case of discrete dynamical system used to study nonlinear phenomena.
G. Pastor +5 more
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Designing a Pseudo-Random Bit Generator Using Generalized Cascade Fractal Function
Chaos Theory and Applications, 2021 A cascade function is designed by combining two seed maps that resultantly has more parameters, high complexity, randomness, and more unpredictable behavior. In the paper, a cascade fractal function, i.e.
Shafali Agarwal
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Coupling Patterns of External Arguments in the Multiple-Spiral Medallions of the Mandelbrot Set
Discrete Dynamics in Nature and Society, 2009 The multiple-spiral medallions are beautiful decorations situated in the proximity of the small copies of the Mandelbrot set. They are composed by an infinity of babies Mandelbrot sets that have external arguments with known structure.
M. Romera +4 more
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Exploration of Filled-In Julia Sets Arising from Centered Polygonal Lacunary Functions
Fractal and Fractional, 2019 Centered polygonal lacunary functions are a particular type of lacunary function that exhibit properties which set them apart from other lacunary functions. Primarily, centered polygonal lacunary functions have true rotational symmetry.
L.K. Mork +4 more
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Mandelbrot and Julia Sets of Transcendental Functions Using Picard–Thakur Iteration
Fractal and Fractional, 2023 The majority of fractals’ dynamical behavior is determined by escape criteria, which utilize various iterative procedures. In the context of the Julia and Mandelbrot sets, the concept of “escape” is a fundamental principle used to determine whether a ...
Ashish Bhoria +2 more
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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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