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Indexed by:Journal Papers

Date of Publication:2016-01-01

Journal:COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

Included Journals:SCIE、EI

Volume:30

Issue:1-3

Page Number:284-298

ISSN No.:1007-5704

Key Words:Julia set; Mandelbrot set; Noise perturbation; Equipotential point algorithm; Fractal

Abstract: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.