Results 31 to 40 of about 6,088,715 (228)
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 ...
Romera, M. +3 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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Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters [PDF]
Journal of The American Mathematical Society, 2017 In the 1980s Branner and Douady discovered a surgery relating various limbs of the Mandelbrot set. We put this surgery in the framework of "Pacman Renormalization Theory" that combines features of quadratic-like and Siegel renormalizations.
Dzmitry Dudko, M. Lyubich, N. Selinger
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Zalcman functions and similarity between the Mandelbrot set, Julia sets, and the tricorn [PDF]
Analysis and Mathematical Physics, 2019 We present a simple proof of Tan’s theorem on asymptotic similarity between the Mandelbrot set and Julia sets at Misiurewicz parameters. Then we give a new perspective on this phenomenon in terms of Zalcman functions, that is, entire functions generated ...
Tomoki Kawahira
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On the Inhomogeneity of the Mandelbrot Set [PDF]
International mathematics research notices, 2018 We will show that the Mandelbrot set $M$ is locally conformally inhomogeneous; the only conformal map $f$ defined in an open set $U$ intersecting $\partial M$ and satisfying $f(U\cap \partial M)=f(U)\cap \partial M$ is the identity map.
Yusheng Luo
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New escape conditions with general complex polynomial for fractals via new fixed point iteration
AIMS Mathematics, 2021 The aim of this paper is to generalize the results regarding fractals and prove escape conditions for general complex polynomial. In this paper we state the orbit of a newly defined iterative scheme and establish the escape criteria in fractal generation
Muhammad Tanveer +4 more
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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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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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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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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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