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Open AccessArticle

Generation of Julia and Madelbrot Sets via Fixed Points

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Department of Mathematics, Government College University, Lahore 54000, Pakistan
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Department of Medical Research, China Medical University No. 91, Hsueh-Shih Road, Taichung 400, Taiwan
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Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, Lahore 54000, Pakistan
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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; https://doi.org/10.3390/sym12010086
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
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Abbas, M.; Iqbal, H.; De la Sen, M. Generation of Julia and Madelbrot Sets via Fixed Points. Symmetry 2020, 12, 86.

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