Results 1 to 10 of about 71,467 (116)

Consensus of Julia Sets

Fractal and Fractional, 2022
The Julia set is one of the most important sets in fractal theory. The previous studies on Julia sets mainly focused on the properties and graph of a single Julia set.
Weihua Sun, Shutang Liu
exaly   +3 more sources

Boundaries of Filled Julia Sets in Generalized Jungck Mann Orbit

IEEE Access, 2019
In this paper, we study the generalized Jungck Mann orbit (GJMO) and prove the converse theorem of results. We develop algorithms for the generation of filled Julia sets and their boundaries in the GJMO.
Muhammad Tanveer, Waqas Nazeer
exaly   +3 more sources

On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals. [PDF]

PLoS One
Our study presents a novel orbit with s-convexity, for illustration of the behavior shift in the fractals. We provide a theorem to demonstrate the escape criterion for transcendental cosine functions of the type Tα,β(u) = cos(um)+αu + β, for [Formula ...
Alam KH, Rohen Y, Saleem N, Aphane M, Razzaque A.   +4 more
europepmc   +2 more sources

Generalized escape criteria for fractals via convex viscosity approximation iterations. [PDF]

PLoS One
In this manuscript, we present the generation of Mandelbrot sets, Julia set fractals, and Biomorphs using a two-step viscosity approximation method applied to the complex function [Formula: see text], where [Formula: see text] and [Formula: see text ...
Wang S, Ahmad K, Yang Y, Cotîrlă LI, Breaz D.   +4 more
europepmc   +2 more sources

Synchronization of Julia Sets in Three-Dimensional Discrete Financial Models

Fractal and Fractional, 2023
When aiming to achieve consistency in fractal characteristics between different models, it is crucial to consider the synchronization of Julia sets.
Zhongyuan Zhao, Yongping Zhang, Dadong Tian   +2 more
doaj   +1 more source

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
doaj   +1 more source

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, Muhammad Tanveer, Muhammad Azhar, Waqas Nazeer, Sania Qureshi   +4 more
doaj   +1 more source

A New Measure of Quantum Starlike Functions Connected with Julia Functions

Journal of Function Spaces, 2022
In a complex domain, the investigation of the quantum differential subordinations for starlike functions is newly considered by few research studies. In this note, we arrange a set of necessary conditions utilizing the concept of the quantum differential
Samir B. Hadid, Rabha W. Ibrahim, Shaher Momani   +2 more
doaj   +1 more source

Visualization of Mandelbrot and Julia Sets of Möbius Transformations

Fractal and Fractional, 2021
This work reports on a study of the Mandelbrot set and Julia set for a generalization of the well-explored function η(z)=z2+λ. The generalization consists of composing with a fixed Möbius transformation at each iteration step.
Leah K. Mork, Darin J. Ulness
doaj   +1 more source

A study of a meromorphic perturbation of the sine family

Demonstratio Mathematica, 2022
We study the dynamics of a meromorphic perturbation of the family λsinz\lambda \sin z by adding a pole at zero and a parameter μ\mu , that is, fλ,μ(z)=λsinz+μ/z{f}_{\lambda ,\mu }\left(z)=\lambda \sin z+\mu \hspace{-0.08em}\text{/}\hspace{-0.08em}z ...
Domínguez Patricia, Vázquez Josué
doaj   +1 more source