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Graphical exploration of the connectivity sets of alternated Julia sets; M, the set of disconnected alternated Julia sets
- Publication Year :
- 2018
- Publisher :
- arXiv, 2018.
-
Abstract
- Using computer graphics and visualization algorithms, we extend in this work the results obtained analytically in [1], on the connectivity domains of alternated Julia sets, defined by switching the dynamics of two quadratic Julia sets. As proved in [1], the alternated Julia sets exhibit, as for polynomials of degree greater than two, the disconnectivity property in addition to the known dichotomy property (connectedness and totally disconnectedness) which characterizes the standard Julia sets. Via computer graphics, we unveil these connectivity domains which are four-dimensional fractals. The computer graphics results show here, without substituting the proof but serving as a research guide, that for the alternated Julia sets, the Mandelbrot set consists of the set of all parameter values, for which each alternated Julia set is not only connected, but also disconnected.<br />Comment: 7 figures
- Subjects :
- Discrete mathematics
Mathematics::Dynamical Systems
Degree (graph theory)
Social connectedness
Mathematics::Complex Variables
Applied Mathematics
Mechanical Engineering
Aerospace Engineering
FOS: Physical sciences
Ocean Engineering
Dynamical Systems (math.DS)
Mandelbrot set
Nonlinear Sciences - Chaotic Dynamics
Julia set
Computer graphics
Set (abstract data type)
Quadratic equation
Fractal
Control and Systems Engineering
FOS: Mathematics
Electrical and Electronic Engineering
Mathematics - Dynamical Systems
Chaotic Dynamics (nlin.CD)
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....52af79d4562f719bcfe9993090b37e0f
- Full Text :
- https://doi.org/10.48550/arxiv.1810.06982