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Switching processes in polynomiography
- 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.
- Subjects :
- Discrete mathematics
Applied Mathematics
Mechanical Engineering
Aerospace Engineering
Ocean Engineering
Polynomiography
dynamics
Mandelbrot set
switching process
01 natural sciences
Julia set
010305 fluids & plasmas
Image (mathematics)
Algebra
Fractal
fractal
Control and Systems Engineering
polynomiography
0103 physical sciences
Convergence tests
Electrical and Electronic Engineering
010301 acoustics
Root-finding algorithm
Complex plane
Mathematics
Subjects
Details
- ISSN :
- 1573269X and 0924090X
- Volume :
- 87
- Database :
- OpenAIRE
- Journal :
- Nonlinear Dynamics
- Accession number :
- edsair.doi.dedup.....4bf705b21a5da96d0de6f7b171fbe152