Results 11 to 20 of about 2,419 (215)
The Symmetry in the Noise-Perturbed Mandelbrot Set [PDF]
Symmetry, 2019 This paper investigates the destruction of the symmetrical structure of the noise-perturbed Mandelbrot set (M-set). By applying the “symmetry criterion” method, we quantitatively compare the damages to the symmetry of the noise-perturbed Mandelbrot set resulting from additive and multiplicative noises.
Sun, Tianwen, Wang, Da
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The Parabolic Mandelbrot Set [PDF]
, 2021 This revised version has 80 pages, 26 ...
Petersen, Carsten Lunde, Roesch, Pascale
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Quadratic dynamics over hyperbolic numbers: a brief survey [PDF]
Surveys in Mathematics and its Applications, 2022 Hyperbolic numbers, also called split complex or perplex numbers in the literature, are a variation of complex numbers established as a theory primarily by W. Clifford in the nineteenth century who applied them to mechanics.
Sandra Hayes
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Exploring parameter spaces in complex dynamics
Selecciones Matemáticas, 2023 We show the structure of the parameter space for a family of rational maps containing Blaschke products. Through numerical simulations using the orbit of a single critical point, we reveal the existence of infinitely many Mandelbrot-like sets along the ...
Pedro Iván Suárez Navarro
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Fractals via Generalized Jungck–S Iterative Scheme
Discrete Dynamics in Nature and Society, 2021 The purpose of this research is to introduce a Jungck–S iterative method with m,h1,h2–convexity and hence unify different comparable iterative schemes existing in the literature.
Zhihua Chen +3 more
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On the Inhomogeneity of the Mandelbrot Set [PDF]
International Mathematics Research Notices, 2019 Abstract 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.
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Anti Mandelbrot Sets via Jungck-M Iteration
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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On the Fibonacci–Mandelbrot set
Indagationes Mathematicae, 2015 Let \(\mathbb{D}:=\{z\in\mathbb{C}\, ; |z|
Sirvent, Víctor F. +1 more
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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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