General escape criteria for the generation of fractals in extended Jungck–Noor orbit

Asifa Tassaddiq

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 196, issue C, 1-14

Abstract: The aesthetic patterns play a key role in the field of fractals. Due to self similarities in the nature of fractals, researchers used the fractals in many fields of sciences (i.e. in Mathematics, Computer Science, Physics, Image Encryption, Biology and Chemistry). The most studied fractals types are the Mandelbrot sets (MSs) and Julia sets (JSs). To generate fractals, escape criteria is required. In this work, a general escape criteria is proved via extended Jungck-Noor iteration with s-convexity. These results are used in algorithms to present the generation of fractals in extended Jungck-Noor orbit for general complex polynomial f(x)=∑i=0paixi with p≥2, where ai∈ℂ for i=0,1,2,…,p. The graphics of MSs and JSs are demonstrated in the examples. The variations in MSs and JSs for different values of involved parameters are also shown.

Keywords: Jungck–Noor orbit; Complex graphics; General escape radius (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475422000039
Full text for ScienceDirect subscribers only

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:eee:matcom:v:196:y:2022:i:c:p:1-14

DOI: 10.1016/j.matcom.2022.01.003

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().