Calculation of Julia Sets by Equipotential Point Algorithm

Sun, Yaqi; Zhao, Xudong; Hou, Kaining

doi:10.1142/s0218127413500156

Cited by 4 publications

(2 citation statements)

References 5 publications

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“…The time when an initial point converges to each periodic point of the Julia set is different [16]. For example, if a point converges to P 1 after 200 iterations, it will converges to P 2 after two 201 iterations, converges to P 3 after 202 iterations, and converges to P 1 after 203 iterations.…”

Section: Numerical Experiments and Analysismentioning

confidence: 99%

Complex time-delay dynamical systems of quadratic polynomials mapping

Sun

2014

Nonlinear Dyn

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Time delays widely exist in the complex dynamical systems. In this paper, time-delay complex dynamical systems are studied by analyzing the properties of corresponding Julia sets. Experimental results show that the stability of complex dynamical system changes greatly due to the influence of time delay. The variations in time-delay Julia sets are studied. In addition, the conditions holding the dynamical systems stable are found. Time delay affects the stability of complex dynamical systems, and the existence of the fixed and periodic points is also discussed.

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Section: Numerical Experiments and Analysismentioning

confidence: 99%

Complex time-delay dynamical systems of quadratic polynomials mapping

Sun

2014

Nonlinear Dyn

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“…This is because many fractals have highlighted characteristics and fit into parallel environments. For example, symmetrical characteristics are owned by many generalized Mandelbrot sets [10, 11], Julia sets [12], and other fractals [13].…”

Section: Introductionmentioning

confidence: 99%

Distributional Fractal Creating Algorithm in Parallel Environment

Liu

Deng

et al. 2013

International Journal of Distributed Sensor Networks

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Nowadays, the fractal is used widely everywhere. Then, its creating time becomes an important study area for complex iteration functions because the escape-time algorithm (ETA), which is the most used algorithm in fractal creating, performs not so well in this condition. In this paper, in order to solve this problem, we improve ETA into the parallel environment and reach well performance. At first, we provide a separation method of ETA to reform it into a SIMC-MC2 grid. Secondly, we prove its correctness and compute the complexity of this novel parallel algorithm. Meantime, we separate an improved ETA which we have presented into the same parallel environment and compute its complexity. Additionally, theoretical and experimental results show the characteristics of this novel algorithm. Finally, the computational result shows that a novel environment is needed to decrease large manual allocation strategies, which block the improved benefit.

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