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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   +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

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

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

Graphical exploration of the connectivity sets of alternated Julia sets [PDF]

Nonlinear Dynamics, 2013
7 ...
Marius-F Danca, Paul Bourke, Danca Marius-F   +2 more
exaly   +3 more sources

Orthogonal Polynomials on Generalized Julia Sets [PDF]

Complex Analysis and Operator Theory, 2017
We extend results by Barnsley et al. about orthogonal polynomials on Julia sets to the case of generalized Julia sets. The equilibrium measure is considered. In addition, we discuss optimal smoothness of Green functions and Parreau-Widom criterion for a special family of real generalized Julia sets.
Alexander Goncharov, Gökalp Alpan
exaly   +6 more sources

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   +3 more sources

Quartic Julia sets including any two copies of quadratic Julia sets

Discrete and Continuous Dynamical Systems, 2016
Let \(P\) be a polynomial of degree \(d\geqslant 2\) and denote by \(K(P)\) the filled-in Julia set of \(P\), which is the set of points that have bounded orbit under iteration by \(P\). It is well-known that if all finite critical points of \(P\) escape to infinity, then \(K(P)\) is totally disconnected, while \(K(P)\) is connected if and only if all ...
exaly   +4 more sources