Results 41 to 50 of about 6,319,108 (303)
Finite Basin's Area Fractal via Complex Newton's Method [PDF]
Kirkuk Journal of Science, 2018 In this study, we explain that when we applied Newton’s method on , the basins of roots have finite area when , where and . Using MATLAB we obtained nice fractals in order to prove the finite basins area when .
Zainab Weli Murad
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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. However, two such maps F
Blanchard, Paul +5 more
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Mandelbrot and Julia Sets of Transcendental Functions Using Picard–Thakur Iteration
Fractal and Fractional, 2023 The majority of fractals’ dynamical behavior is determined by escape criteria, which utilize various iterative procedures. In the context of the Julia and Mandelbrot sets, the concept of “escape” is a fundamental principle used to determine whether a ...
Ashish Bhoria +2 more
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Graphical exploration of the connectivity sets of alternated Julia sets [PDF]
Nonlinear Dynamics, 2013 7 ...
Danca, Marius-F. +2 more
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Background The Standards for Psychosocial Care for Children with Cancer and Their Families guide the provision of comprehensive psychosocial care. Parallel to research characterizing implementation of the Standards from the perspective of providers, this study examines implementation of the Standards from the perspective of parents of youth ...
Emily M. Pariseau +8 more
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Analysis of Neutrosophic Set, Julia Set in Aircraft Crash
Neutrosophic Sets and SystemsA neutrosophic fuzzy set that generalizes the classical set is represented by a closed interval [0,1]. Let us generalize the fuzzy set to the Neutrosophic set, which is defined as three membership functions between interval ]-0,1+ [.
M.N. Bharathi, G. Jayalalitha
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Quadratic dynamics over hyperbolic numbers: a brief survey [PDF]
Surveys in Mathematics and its Applications, 2022 Hyperbolic numbers, also called split complex or perplex numbers in the literature, are a variation of complex numbers established as a theory primarily by W. Clifford in the nineteenth century who applied them to mechanics.
Sandra Hayes
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