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Switching processes in polynomiography

Authors :
Krzysztof Gdawiec
Source :
Nonlinear Dynamics. 87:2235-2249
Publication Year :
2016
Publisher :
Springer Science and Business Media LLC, 2016.

Abstract

Mandelbrot and Julia sets are examples of fractal patterns generated in the complex plane. In the literature we can find many generalizations of those sets. One of such generalizations is the use of switching process. In this paper we introduce some switching processes to another type of complex fractals, namely polynomiographs. Polynomiograph is an image presenting the visualization of the complex polynomial's root finding process. The proposed switching processes will be divided into four groups, i.e., switching of: the root finding methods, the iterations, the polynomials and the convergence tests. All the proposed switching processes change the dynamics of the root finding process and allowed us to obtain new and diverse fractal patterns.

Details

ISSN :
1573269X and 0924090X
Volume :
87
Database :
OpenAIRE
Journal :
Nonlinear Dynamics
Accession number :
edsair.doi.dedup.....4bf705b21a5da96d0de6f7b171fbe152