Results 1 to 10 of about 1,964,264 (277)

Consensus of Julia Sets [PDF]

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
doaj   +3 more sources

Julia and Mandelbrot Sets for Dynamics over the Hyperbolic Numbers

Fractal and Fractional, 2019
Julia and Mandelbrot sets, which characterize bounded orbits in dynamical systems over the complex numbers, are classic examples of fractal sets. We investigate the analogs of these sets for dynamical systems over the hyperbolic numbers.
Vance Blankers, Tristan Rendfrey, Aaron Shukert, Patrick D. Shipman   +3 more
doaj   +4 more sources

An image encryption algorithm utilizing julia sets and hilbert curves. [PDF]

PLoS ONE, 2014
Image encryption is an important and effective technique to protect image security. In this paper, a novel image encryption algorithm combining Julia sets and Hilbert curves is proposed.
Yuanyuan Sun, Lina Chen, Rudan Xu, Ruiqing Kong   +3 more
doaj   +2 more sources

A study of Mandelbrot and Julia Sets via Picard-Thakur iteration with s-convexity. [PDF]

PLoS ONE
Nowadays, many researchers are employing various iterative techniques to analyse the dynamics of fractal patterns. In this paper, we explore the formation of Mandelbrot and Julia sets using the Picard-Thakur iteration process, extended with s-convexity ...
Bashir Nawaz, Krzysztof Gdawiec, Kifayat Ullah, Maggie Aphane   +3 more
doaj   +2 more sources

Computer Visualization of Julia Sets for Maps beyond Complex Analyticity [PDF]

EPJ Web of Conferences, 2021
Using the computer program creating Julia sets for two-dimensional maps we have made computer animation showing how Julia sets for the Peckham map alters when the parameter of the map is changing. The Peckham map is a one-parameter map which includes the
Toporensky Alexey, Stepanyan Ivan
doaj   +3 more sources

Mandelbrot Sets and Julia Sets in Picard-Mann Orbit

IEEE Access, 2020
The purpose of this paper is to introduce the Mandelbrot and Julia sets by using Picard-Mann iteration procedure. Escape criteria is established which plays an important role to generate Mandelbrot and Julia sets.
Cui Zou, Abdul Aziz Shahid, Asifa Tassaddiq, Arshad Khan, Maqbool Ahmad   +4 more
doaj   +3 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   +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 ...
Shuai Wang, Khaleel Ahmad, Yining Yang, Luminiţa-Ioana Cotîrlă, Daniel Breaz   +4 more
doaj   +2 more sources

Mandelbrot Set as a Particular Julia Set of Fractional Order, Equipotential Lines and External Rays of Mandelbrot and Julia Sets of Fractional Order

Fractal and Fractional
This paper deepens some results on a Mandelbrot set and Julia sets of Caputo’s fractional order. It is shown analytically and computationally that the classical Mandelbrot set of integer order is a particular case of Julia sets of Caputo-like fractional ...
Marius-F. Danca
doaj   +3 more sources

Adaptive anti-synchronization of transcendental alternated system of Julia sets [PDF]

Scientific Reports
This paper presents an adaptive control strategy for achieving anti-synchronization in transcendental alternated(odd and even functions) Julia sets.
Varthini Ravikumar, Pulak Konar
doaj   +2 more sources