{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,21]],"date-time":"2026-06-21T13:08:48Z","timestamp":1782047328466,"version":"3.54.5"},"reference-count":45,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,2]],"date-time":"2020-07-02T00:00:00Z","timestamp":1593648000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>There is a huge group of algorithms described in the literature that iteratively find solutions of a given equation. Most of them require tuning. The article presents root-finding algorithms that are based on the Newton\u2013Raphson method which iteratively finds the solutions, and require tuning. The modification of the algorithm implements the best position of particle similarly to the particle swarm optimisation algorithms. The proposed approach allows visualising the impact of the algorithm\u2019s elements on the complex behaviour of the algorithm. Moreover, instead of the standard Picard iteration, various feedback iteration processes are used in this research. Presented examples and the conducted discussion on the algorithm\u2019s operation allow to understand the influence of the proposed modifications on the algorithm\u2019s behaviour. Understanding the impact of the proposed modification on the algorithm\u2019s operation can be helpful in using it in other algorithms. The obtained images also have potential artistic applications.<\/jats:p>","DOI":"10.3390\/e22070734","type":"journal-article","created":{"date-parts":[[2020,7,3]],"date-time":"2020-07-03T06:51:20Z","timestamp":1593759080000},"page":"734","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1315-6082","authenticated-orcid":false,"given":"Ireneusz","family":"Go\u015bciniak","sequence":"first","affiliation":[{"name":"Institute of Computer Science, University of Silesia, B\u0229dzi\u0144ska 39, 41\u2013200 Sosnowiec, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9434-9307","authenticated-orcid":false,"given":"Krzysztof","family":"Gdawiec","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, University of Silesia, B\u0229dzi\u0144ska 39, 41\u2013200 Sosnowiec, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,2]]},"reference":[{"key":"ref_1","unstructured":"Polak, E. 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