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Chaotic bands in the Mandelbrot set

AuthorsPastor, Gerardo; Romera, Miguel; Álvarez Marañón, Gonzalo; Montoya Vitini, Fausto
KeywordsMandelbrot set
Chaotic bands
Hyperbolic components ordering
Misiurewicz points ordering
Issue Date13-Aug-2004
CitationComputers & Graphics 28(5): 779-784 (2004)
AbstractHyperbolic 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, shrub(0), corresponds to the main branch of the shrub. The second one, shrub(r), 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 shrub(0) of any shrub of the Mandelbrot set. We have seen that each shrub(0) 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.
Description6 pages, 5 figures.-- PACS nr.: 05.45.+b.-- Printed version published on Oct 2004.
Publisher version (URL)http://dx.doi.org/10.1016/j.cag.2004.06.015
Appears in Collections:(IFA) Artículos
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