Results 31 to 40 of about 6,319,108 (303)
Fractal Dimension Analysis of the Julia Sets of Controlled Brusselator Model
Discrete Dynamics in Nature and Society, 2016 Fractal theory is a branch of nonlinear scientific research, and its research object is the irregular geometric form in nature. On account of the complexity of the fractal set, the traditional Euclidean dimension is no longer applicable and the ...
Yuqian Deng +2 more
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Singular Perturbations of Multibrot Set Polynomials
Universal Journal of Mathematics and Applications, 2022 We will give a complete description of the dynamics of the rational map $N_{F_{M_c}}(z)=\frac{3z^4-2z^3+c}{4z^3-3z^2+c}$ where c is a complex parameter. These are rational maps $N_{F_{M_c}}$ arising from Newton's method.
Figen Çilingir
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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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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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On the Fractional-Order Complex Cosine Map: Fractal Analysis, Julia Set Control and Synchronization
Mathematics, 2023 In this paper, we introduce a generalized complex discrete fractional-order cosine map. Dynamical analysis of the proposed complex fractional order map is examined. The existence and stability characteristics of the map’s fixed points are explored.
A. A. Elsadany +3 more
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Fractal and Fractional, 2021 In this paper, a novel escape-time algorithm is proposed to calculate the connectivity’s degree of Julia sets generated from polynomial maps. The proposed algorithm contains both quantitative analysis and visual display to measure the connectivity of ...
Yang Zhao +3 more
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Julia set generation pseudocode.
, 2014 Julia set generation pseudocode.
Ruiqing Kong (505631) +3 more
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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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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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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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