Results 31 to 40 of about 6,037,193 (187)

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, M. Romera, G. Alvarez, J. Nunez, D. Arroyo, F. Montoya   +5 more
doaj   +1 more source

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, Trenton Vogt, Keith Sullivan, Drew Rutherford, Darin J. Ulness   +4 more
doaj   +1 more source

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
doaj   +1 more source

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, G. Pastor, A. B. Orue, D. Arroyo, F. Montoya   +4 more
doaj   +1 more source

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, Anju Panwar, Mohammad Sajid   +2 more
doaj   +1 more source

Characterization of the Principal 3D Slices Related to the Multicomplex Mandelbrot Set [PDF]

Advances in Applied Clifford Algebras, 2018
This article focuses on the dynamics of the different tridimensional principal slices of the multicomplex Multibrot sets. First, we define an equivalence relation between those slices. Then, we characterize them in order to establish similarities between
Guillaume Brouillette, D. Rochon
semanticscholar   +1 more source

Escape Criteria for Generating Fractals of Complex Functions Using DK-Iterative Scheme

Fractal and Fractional, 2023
Fractals are essential in representing the natural environment due to their important characteristic of self similarity. The dynamical behavior of fractals mostly depends on escape criteria using different iterative techniques.
Asifa Tassaddiq, Muhammad Tanveer, Muhammad Azhar, Muhammad Arshad, Farha Lakhani   +4 more
doaj   +1 more source

Performing a multi-stage mathematical information task "Framing the Mandelbrot set of families of polynomials of the third degree and remarkable curves"

Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics
In this article, within the framework of a multi-stage mathematical information task, the methodology for students to study Mandelbrot sets and frames of Mandelbrot sets of a family of polynomials of the third degree is indicated.
Elena Sa. Smirnova, V. Sekovanov, L. B. Rybina, R. A. Shchepin   +3 more
semanticscholar   +1 more source

The Proof of a Conjecture Relating Catalan Numbers to an Averaged Mandelbrot-Möbius Iterated Function

Fractal and Fractional, 2021
In 2021, Mork and Ulness studied the Mandelbrot and Julia sets for a generalization of the well-explored function ηλ(z)=z2+λ. Their generalization was based on the composition of ηλ with the Möbius transformation μ(z)=1z at each iteration step ...
Pavel Trojovský, K Venkatachalam
doaj   +1 more source

Performing a Multi-Stage Mathematical and Informational Task "Framing the First-Order Mandelbrot Set, Julia Sets, the Structure of Fixed Points of a Family of Polynomials of the Third Degree" as a Means of Developing Students' Creativity

Современные информационные технологии и IT-образование
The article deals with issues from the field of nonlinear dynamics, in particular, such a section of it as holomorphic dynamics. We believe that the Mandelbrot set and the Julia set are important objects of holomorphic dynamics research.
Valeriy Sekovanov, Vladimir Ivkov, Elena Smirnova, Larisa Rybina   +3 more
doaj   +1 more source