Results 31 to 40 of about 66,338 (262)
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 +3 more
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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
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Julia sets are uniformly perfect [PDF]
Proceedings of the American Mathematical Society, 1992 We prove that Julia sets are uniformly perfect in the sense of Pommerenke (Arch. Math. 32 (1979), 192-199). This implies that their linear density of logarithmic capacity is strictly positive, thus implying that Julia sets are regular in the sense of Dirichlet.
Mañé, R., Da Rocha, L. F.
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Application of the Fractal Geometry in Development Surya Majapahit Batik Motif
JTAM (Jurnal Teori dan Aplikasi Matematika)The Mandelbrot and Julia sets are generated through iterative mathematical functions applied to points in the complex plane. These operations enable the detailed and intricate patterns characteristic of these fractals, allowing for modifications and ...
Juhari Juhari +1 more
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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 +4 more
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Julia sets and differential equations [PDF]
Proceedings of the American Mathematical Society, 1993 Summary: A one-parameter family of Julia sets is shown to converge, in a probabilistic sense, to certain trajectories of a differential equation. The Julia sets arise from Euler's method for the differential equation. This provides information on the location of the Julia sets and the dynamics on them.
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Julia Sets in Parameter Spaces [PDF]
Communications in Mathematical Physics, 2001 The paper is devoted to study the one parameter family of cubic polynomials \[ g_b(z)= \lambda z+ bz^2+z^3, \quad b\in \mathbb{C},\tag{1} \] where \(\lambda= e^{2\pi i\theta}\) is a fixed complex number of modulus 1. The authors show that the bifurcation locus of (1) contains quasi-conformal copies of the quadratic Julia set \(J(\lambda z+z^2)\).
Buff, X., Henriksen, C.
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CHECKERBOARD JULIA SETS FOR RATIONAL MAPS [PDF]
International Journal of Bifurcation and Chaos, 2013 In this paper, we consider the family of rational maps [Formula: see text] where n ≥ 2, d ≥ 1, and λ ∈ ℂ. We consider the case where λ lies in the main cardioid of one of the n - 1 principal Mandelbrot sets in these families. We show that the Julia sets of these maps are always homeomorphic.
Blanchard, Paul +5 more
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Fractal and FractionalThis 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
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International Journal of Mathematics and Mathematical Sciences, 2001 In 1977 Hubbard developed the ideas of Cayley (1879) and solved in particular the Newton-Fourier imaginary problem. We solve the Newton-Fourier and the Chebyshev-Fourier imaginary problems completely.
Anna Tomova
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