Comparative Study of Some Fixed-Point Methods in the Generation of Julia and Mandelbrot Sets

Hao Zhou, Muhammad Tanveer, Jingjng Li and Basil K. Papadopoulos

Journal of Mathematics, 2020, vol. 2020, 1-15

Abstract: Fractal is a geometrical shape with property that each point of the shape represents the whole. Having this property, fractals procured the attention in computer graphics, engineering, biology, mathematics, physics, art, and design. The fractals generated on highest priorities are the Julia and Mandelbrot sets. So, in this paper, we develop some necessary conditions for the convergence of sequences established for the orbits of M, M∗, and K-iterative methods to generate these fractals. We adjust algorithms according to the develop conditions and draw some attractive Julia and Mandelbrot sets with sequences of iterates from proposed fixed-point iterative methods. Moreover, we discuss the self-similarities with input parameters in each graph and present the comparison of images with proposed methods.

Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2020/7020921.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2020/7020921.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7020921

DOI: 10.1155/2020/7020921

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().