Results 41 to 50 of about 29,416 (289)
, 2016 The pictures show Julia sets consisting of points generated by iterating the complex number transformation z→{√z-c,-√z-c}, starting at z=0. The Mandelbrot set can be defined as the set of values of c for which such Julia sets are connectedEducação ...
Wolfram, Stephen
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Control and synchronization of Julia sets of the complex dissipative standard system
Nonlinear Analysis, 2016 The fractal behaviors of the complex dissipative standard system are discussed in this paper. By using the boundedness of the forward and backward orbits, Julia set of the system is introduced and visualization of Julia set is also given.
Weihua Sun, Yongping Zhang
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, 2013 The pictures show Julia sets consisting of points generated by iterating the complex number transformation z→{√z-c,-√z-c}, starting at z=0. The Mandelbrot set can be defined as the set of values of c for which such Julia sets are connectedEducação ...
Wolfram, Stephen
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LINEAR GENERALIZED SYNCHRONIZATION OF SPATIAL JULIA SETS [PDF]
, 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 ...
CHANGAN LIU, PING LIU
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Fractal Generation in Modified Jungck–S Orbit
IEEE Access, 2019 The aim of this paper is to modify the Jungck-S iterative scheme by adding the idea of s-convexity. We define and analyze the modified Jungck-S orbit (MJSO) with s-convex combination and derive the escape criterion for MJSO.
Young Chel Kwun +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 dimension of the universal Julia sets for the Chebyshev-Halley family of methods [PDF]
, 2011 The concept of universal Julia set introduced in [5] allows us to conclude that the dynamics of a root-finding algorithm applied to any quadratic polynomial can be understood through the analysis of a particular rational map.
Varona, J.L. [0000-0002-2023-9946] +2 more
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Fractals Parrondo’s Paradox in Alternated Superior Complex System
Fractal and Fractional, 2021 This work focuses on a kind of fractals Parrondo’s paradoxial phenomenon “deiconnected+diconnected=connected” in an alternated superior complex system zn+1=β(zn2+ci)+(1−β)zn,i=1,2.
Yi Zhang, Da Wang
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