Results 21 to 30 of about 6,037,193 (187)
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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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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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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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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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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Local Connectivity of the Mandelbrot Set at Some Satellite Parameters of Bounded Type [PDF]
Geometric and Functional Analysis, 2018 We explore geometric properties of the Mandelbrot set M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
Dzmitry Dudko, M. Lyubich
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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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Teaching Mathematics and its Applications: An International Journal of the IMA, 2020 Mathematics undergraduates often encounter a variety of digital representations which are more idiosyncratic than the ones they have experienced in school and which often require the use of more sophisticated digital tools.
R. Miles
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Resting-State Functional MRI Analyses for Brain Activity Characterization: A Narrative Review of Features and Methods. [PDF]
Eur J NeurosciFunctional connectivity is a popular resting‐state functional MRI analysis. Nevertheless, there are alternative approaches that can be used to characterize the BOLD signal differently, which allow for indirect characterization of brain activity, focusing on regional connectivity, intensity, and complexity.
Amador-Tejada A +3 more
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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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