Significant Curves of the Mandelbrot Set
Abstract
The paper provides a description of some interesant curves contained in the Mandelbrot set. These curves are the boundaries of the areas called „bulbs“ which are described approximately only in present. In this paper, some of them are described analyticaly – curves of so called first period, the boundary of the main hyperbolic component, internal and external bounds and also some curves of the second period.
References
Devaney, R. The fractal geometry of the mandelbrot set ii: How to add and how to count. Fractals 03, 04 (1995), 629–650.
Devaney, R. Unveiling the mandelbrot set. Plus Magazine 40 (2006).
Douady, A., and Hubbard, J. H. It´eration des polynˆomes quadratiques complexes (iteration of complex quadratic polynomials). C. R. Acad. Sci., Paris, S´er. I 294 (1982), 123–125.
Fowler, A., and McGuinness, M. The size of mandelbrot bulbs. Chaos, Solitons Fractals: X 3 (2019), 100019.
Goldberg, L., and Tresser, C. Rotation orbits and the farey tree. Ergodic Theory and Dynamical Systems 16, 5 (1996), 1011–1029.
Copyright (c) 2021 MENDEL
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
MENDEL open access articles are normally published under a Creative Commons Attribution-NonCommercial-ShareAlike (CC BY-NC-SA 4.0) https://creativecommons.org/licenses/by-nc-sa/4.0/ . Under the CC BY-NC-SA 4.0 license permitted 3rd party reuse is only applicable for non-commercial purposes. Articles posted under the CC BY-NC-SA 4.0 license allow users to share, copy, and redistribute the material in any medium of format, and adapt, remix, transform, and build upon the material for any purpose. Reusing under the CC BY-NC-SA 4.0 license requires that appropriate attribution to the source of the material must be included along with a link to the license, with any changes made to the original material indicated.