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The Symmetry in the Noise-Perturbed Mandelbrot Set

Research Center of Dynamics System and Control Science, Shandong Normal University, Jinan 250014, China
Author to whom correspondence should be addressed.
Symmetry 2019, 11(4), 577;
Received: 22 March 2019 / Revised: 12 April 2019 / Accepted: 17 April 2019 / Published: 21 April 2019
PDF [4078 KB, uploaded 25 April 2019]


This paper investigates the destruction of the symmetrical structure of the noise-perturbed Mandelbrot set (M-set). By applying the “symmetry criterion” method, we quantitatively compare the damages to the symmetry of the noise-perturbed Mandelbrot set resulting from additive and multiplicative noises. Because of the uneven distribution between the core positions and the edge positions of the noise-perturbed Mandelbrot set, the comparison results reveal a paradox between the visual sense and quantified result. Thus, we propose a new “visual symmetry criterion” method that is more suitable for the measurement of visual asymmetry. View Full-Text
Keywords: symmetry destruction; Mandelbrot set; noise; fractals; social network symmetry destruction; Mandelbrot set; noise; fractals; social network

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Sun, T.; Wang, D. The Symmetry in the Noise-Perturbed Mandelbrot Set. Symmetry 2019, 11, 577.

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