Next Article in Journal
Computer-Aided Laser-Fiber Output Beam 3D Spatial and Angular Design
Previous Article in Journal
RDF 1.1: Knowledge Representation and Data Integration Language for the Web
Previous Article in Special Issue
The Asymmetric Alpha-Power Skew-t Distribution
Open AccessArticle

Generation of Julia and Madelbrot Sets via Fixed Points

Department of Mathematics, Government College University, Lahore 54000, Pakistan
Department of Medical Research, China Medical University No. 91, Hsueh-Shih Road, Taichung 400, Taiwan
Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, Lahore 54000, Pakistan
Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia), P.O. Box 644, Bilbao, Barrio Sarriena, 48940 Leioa, Spain
Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 86;
Received: 27 November 2019 / Revised: 24 December 2019 / Accepted: 26 December 2019 / Published: 2 January 2020
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
The aim of this paper is to present an application of a fixed point iterative process in generation of fractals namely Julia and Mandelbrot sets for the complex polynomials of the form T ( x ) = x n + m x + r where m , r C and n 2 . Fractals represent the phenomena of expanding or unfolding symmetries which exhibit similar patterns displayed at every scale. We prove some escape time results for the generation of Julia and Madelbrot sets using a Picard Ishikawa type iterative process. A visualization of the Julia and Mandelbrot sets for certain complex polynomials is presented and their graphical behaviour is examined. We also discuss the effects of parameters on the color variation and shape of fractals. View Full-Text
Keywords: iteration; fixed points; fractals iteration; fixed points; fractals
Show Figures

Figure 1

MDPI and ACS Style

Abbas, M.; Iqbal, H.; De la Sen, M. Generation of Julia and Madelbrot Sets via Fixed Points. Symmetry 2020, 12, 86.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Back to TopTop