{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T18:18:48Z","timestamp":1777054728168,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,18]],"date-time":"2024-03-18T00:00:00Z","timestamp":1710720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Iterative procedures have been proved as a milestone in the generation of fractals. This paper presents a novel approach for generating and visualizing fractals, specifically Mandelbrot and Julia sets, by utilizing complex polynomials of the form QC(p)=apn+mp+c, where n\u22652. It establishes escape criteria that play a vital role in generating these sets and provides escape time results using different iterative schemes. In addition, the study includes the visualization of graphical images of Julia and Mandelbrot sets, revealing distinct patterns. Furthermore, the study also explores the impact of parameters on the deviation of dynamics, color, and appearance of fractals.<\/jats:p>","DOI":"10.3390\/axioms13030204","type":"journal-article","created":{"date-parts":[[2024,3,18]],"date-time":"2024-03-18T04:25:15Z","timestamp":1710735915000},"page":"204","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Generating Geometric Patterns Using Complex Polynomials and Iterative Schemes"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6165-8055","authenticated-orcid":false,"given":"Asifa","family":"Tassaddiq","sequence":"first","affiliation":[{"name":"Department of Basic Sciences and Humanities, College of Computer and Information Sciences, Majmaah University, Al-Majmaah 11952, Saudi Arabia"}]},{"given":"Amna","family":"Kalsoom","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2961-1609","authenticated-orcid":false,"given":"Maliha","family":"Rashid","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan"}]},{"given":"Kainat","family":"Sehr","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1275-2384","authenticated-orcid":false,"given":"Dalal Khalid","family":"Almutairi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,18]]},"reference":[{"key":"ref_1","unstructured":"Rassias, T.M. 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