On a topological closeness of perturbed Mandelbrot sets |
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| Authors: | Ioannis Andreadis |
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| Affiliation: | a International School of The Hague, Wijndaelerduin 1, 2554 BX The Hague, The Netherlands
b Department of Civil Engineering, University of Thessaly, GR-38334 Volos, Greece |
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| Abstract: | In the present work we propose a numerical and visual tool for the study of the deformation of the Mandelbrot sets of perturbed Mandelbrot maps by noise in comparison with the original Mandelbrot set. Further, by employing these numerical tools, we support the invariance of the Mandelbrot set of a noise-perturbed Mandelbrot map under different noise realizations. Finally, we provide evidence for the non-fractal structure of the Mandelbrot set of a noise-perturbed Mandelbrot map. |
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| Keywords: | Mandelbrot set Additive dynamic noise Mandelbrot map Distance Deviation plot Fractal |
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