Gerardo Pastor Dégano

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We introduce shrubs in this paper in order to present a first approach to studying the structure of the Mandelbrot set. Primary, secondary ... and N -ary shrubs are analyzed. We have experimentally obtained formulae to calculate the periods of the hyperbolic components representatives of the structural branches, and the preperiods and periods of both the(More)
In this paper we present the alternated Julia sets, obtained by alternated iteration of two maps of the quadratic family 2 1 , 1,2 n n i z z c i     and prove analytically and computationally that these sets can be connected, disconnected or totally disconnected verifying the known Fatou-Julia theorem in the case of polynomials of degree greater than(More)
The authors report their experience with the use of biopsy guns for the histologic sampling of breast lesions. Cytologic sampling by means of FNAB has been preferred so far because it was thought to be simpler, less risky and more reliable. Nevertheless, cytologic sampling exhibits several drawbacks--e.g., the need of repeated punctures to get sufficient(More)
Near to the cusp of a cardioid of the Mandelbrot set, except for the main cardioid, there is a sequence of baby Mandelbrot sets. Each baby Mandelbrot set is in the center of a Douady cauliflower, a decoration constituted by an infinity of minute Mandelbrot sets and Misiurewicz points linked by filaments. A Douady cauliflower appears to have a complicated(More)
This article describes a new family of cryptographically secure pseudorandom number generators, based on coupled chaotic maps, that will serve as keystream in a stream cipher. The maps are a modification of a piecewise linear map, by dynamic changing of the coefficient values and perturbing its lesser significant bits.
Hyperbolic 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(More)
The multiple-spiral medallions are beautiful decorations of the Mandelbrot set. Computer graphics provide an invaluable tool to study the structure of these decorations with central symmetry, formed by an infinity of baby Mandelbrot sets that have high periods. Up to now, the external arguments of the external rays landing at the cusps of the cardioids of(More)
The multiple-spiral medallions are beautiful decorations situated in the proximity of the small copies of the Mandelbrot set. They are composed by an infinity of babies Mandelbrot sets that have external arguments with known structure. In this paper we study the coupling patterns of the external arguments of the baby Mandelbrot sets in multiple-spiral(More)