The symmetry in the noise-perturbed Mandelbrot set (Q2337970)

Summary: 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.