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Linear Generalized Synchronization of Spatial Julia Sets
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2011 In this paper, the generalized synchronization of spatial Julia sets is investigated by applying linear coupling. We achieve the generalized synchronization of two different spatial Julia sets and also obtain the stable domain of the coupling strength ...
Ping Liu, Changan Liu
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Graphical Exploration of the Connectivity Sets of Alternated Julia Sets [PDF]
Nonlinear Dynamics, 2013 7 ...
Marius-F Danca, Paul Bourke
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Journal of Mathematical Sciences, 2020
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Julia sets converging to filled quadratic Julia sets
Ergodic Theory and Dynamical Systems, 2012AbstractIn this paper we consider singular perturbations of the quadratic polynomial $F(z) = z^2 + c$ where $c$ is the center of a hyperbolic component of the Mandelbrot set, i.e., rational maps of the form $z^2 + c + \lambda /z^2$. We show that, as $\lambda \rightarrow 0$, the Julia sets of these maps converge in the Hausdorff topology to the filled ...
Kozma, Robert T., Devaney, Robert L.
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The Mathematical Intelligencer, 1990
The author describes an algorithm for computing the Euclidean symmetry group of the Julia set of a given polynomial. It is based on his paper in Bull. Lond. Math. Soc. 22, No. 2, 576-582 (1990; Zbl 0725.30014).
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The author describes an algorithm for computing the Euclidean symmetry group of the Julia set of a given polynomial. It is based on his paper in Bull. Lond. Math. Soc. 22, No. 2, 576-582 (1990; Zbl 0725.30014).
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Computers & Graphics, 1989
Abstract Recent mathematical work on the dynamics of complex analytic functions has given rise to a new subject matter for computer graphics. The combination of mathematical theory and computer graphics has resulted in new insight into the nature of some of the simplest of mathematical objects. second-degree polynomials. Most of that work has focused
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Abstract Recent mathematical work on the dynamics of complex analytic functions has given rise to a new subject matter for computer graphics. The combination of mathematical theory and computer graphics has resulted in new insight into the nature of some of the simplest of mathematical objects. second-degree polynomials. Most of that work has focused
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Cayley’s problem and Julia sets
The Mathematical Intelligencer, 1984The goal of this exposition is to give a flavor of the subject of Julia Sets which we trace back to a problem posed by \textit{A. Cayley} [Am. J. Math. 2, 97 (1879)]. Our computer graphics not only illustrated the beauty that can be found in Julia sets, but they also provided us with insight that led us to some new results.
Peitgen, H. O. +2 more
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The Polynomials Associated with a Julia Set
Bulletin of the London Mathematical Society, 1995Let \(J\) be the Julia set of some polynomial. The authors show that, except in the case when \(J\) is a circle or straight line, then the set of all polynomials which have \(J\) for their Julia set is given by \(\{\sigma p^n,n \in \mathbb{N}, \sigma \in \Sigma\}\) where \(p\) is one of these polynomials with lowest degree, \(\Sigma\) is the set of ...
Schmidt, W., Steinmetz, N.
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Applied Mathematics and Computation, 2023
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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 ...
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