Chaotic bands in the Mandelbrot set
2004; Elsevier BV; Volume: 28; Issue: 5 Linguagem: Inglês
10.1016/j.cag.2004.06.015
ISSN1873-7684
AutoresG. Pastor, M. Romera, Gonzalo Álvarez, F. Montoya,
Tópico(s)Chaos-based Image/Signal Encryption
ResumoHyperbolic components and Misiurewicz points of the chaotic region of the Mandelbrot set are located in what we call shrubs. Each shrub has two well-differentiated parts. The first one, shrub0, corresponds to the main branch of the shrub. The second one, shrubr, corresponds to all the other branches of the shrub. In this paper, we have focused on the ordering of the hyperbolic components and Misiurewicz points located at the shrub0 of any shrub of the Mandelbrot set. We have seen that each shrub0 is made up of infinite chaotic bands, each one corresponding to a disk of the period-doubling cascade of the hyperbolic component from where the shrub originates.
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