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论文类型：期刊论文

发表时间：2016-01-01

发表刊物：COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

收录刊物：SCIE、EI

卷号：30

期号：1-3

页面范围：284-298

ISSN号：1007-5704

关键字：Julia set; Mandelbrot set; Noise perturbation; Equipotential point algorithm; Fractal

摘要：As the classical ones among the fractal sets, Julia set (abbreviated as J set) and Mandelbrot set (abbreviated as M set) have been explored widely in recent years. In this study, J set and M set under additive noise perturbation and multiplicative noise perturbation are created by equipotential point algorithm. Changes of the J set and M set under random noise perturbation as well as the close correlation between them are studied. Experimental results show that either additive noise perturbation or multiplicative noise perturbation may cause dramatic changes on J set. On the other hand, when the M set is perturbed by additive noise, it almost changes nothing but its position; when the M set is perturbed by multiplicative noise, its inner structures change with the stabilized areas shrinking, but it keeps the symmetry with respect to X axis. In addition, the J set and the M set still share the same stabilized periodic point in spite of noise perturbation. (C) 2015 The Authors. Published by Elsevier B.V.