{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:36:23Z","timestamp":1760142983344,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,2]],"date-time":"2024-01-02T00:00:00Z","timestamp":1704153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"RUDN University Scientific Projects Grant System","award":["202235-2-000"],"award-info":[{"award-number":["202235-2-000"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>New molecular genetic algorithms, as tools for the visualization and analysis of big data, have made it possible not only to illustrate the internal structure of DNA molecules within their parameters but also to explore the field of chaos theory, particularly to display processes and signals close to chaotic ones. This provides a new perspective on the problem of determining criteria for borderline states between order and chaos. This article demonstrates the differences between chaotic and quasi-chaotic signals when visualized with molecular genetic algorithms. It presents examples of molecular genetic mappings of signals generated using various pseudorandom noise generators, as well as acoustic signals. This article considers structural and integral (folded) mappings as one-dimensional and two-dimensional projections of the pattern. The authors illustrate the internal structure of the reconstructed signal mappings in spaces of fractional dimensionality, which is considered as a visualization of the entropy structure based on functional mappings in spaces of the fractional dimension. As a result of this research, it was found that the use of molecular genetic algorithms for visualizing information signals makes it possible to identify the so-called entropy structure of these signals. At the same time, the entropy structure of chaotic signals is absent.<\/jats:p>","DOI":"10.3390\/sym16010059","type":"journal-article","created":{"date-parts":[[2024,1,2]],"date-time":"2024-01-02T03:33:33Z","timestamp":1704166413000},"page":"59","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Visualization of the Signals Entropy Structure Based on Walsh\u2013Hadamard Functions"],"prefix":"10.3390","volume":"16","author":[{"given":"Ivan V.","family":"Stepanyan","sequence":"first","affiliation":[{"name":"Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), 4, M. Kharitonyevskiy Pereulok, 101990 Moscow, Russia"},{"name":"Peoples\u2019 Friendship University of Russia (RUDN University), 6, Miklukho-Maklaya Street, 117198 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5919-0190","authenticated-orcid":false,"given":"Michail Y.","family":"Lednev","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), 4, M. Kharitonyevskiy Pereulok, 101990 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Stepanyan, I.V., and Lednev, M.Y. (2023). Chromatic Differentiation of Functional Mappings of the Composition of Nucleic Acids. Symmetry, 15.","DOI":"10.3390\/sym15040942"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Stepanyan, I.V., and Lednev, M.Y. (2022). Parametric Multispectral Mappings and Comparative Genomics. Symmetry, 14.","DOI":"10.3390\/sym14122517"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Stepanyan, I.V., and Lednev, M.Y. (2022). A Comparative Analysis of Different Strains of Coronavirus Based on Genometric Mappings. Symmetry, 14.","DOI":"10.3390\/sym14050942"},{"key":"ref_4","unstructured":"Tverdislov, V.A., Sidorova, A.E., and Yakovenko, L.V. (2012). Biophysical Ecology, URSS, KRASAND."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gupta, V., Mittal, M., and Mittal, V. (2020). Chaos theory: An emerging tool for arrhythmia detection. Sens. Imaging, 21.","DOI":"10.1007\/s11220-020-0272-9"},{"key":"ref_6","unstructured":"Singh, A.P., Kumar, G., Dhillon, G.S., and Taneja, H. (2023). Evolutionary Intelligence, Springer."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Puntsri, K., Bunsri, B., Pittayang, Y., Bubpawan, T., Partipralam, W., and Phakphisut, W. (2022, January 5\u20138). Reconfigurable AWGN Generator Using Box-Muller Method with CORDIC-Based Square Root Calculation. Proceedings of the 2022 37th International Technical Conference on Circuits\/Systems, Computers and Communications (ITC-CSCC), Phuket, Thailand.","DOI":"10.1109\/ITC-CSCC55581.2022.9894924"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3354","DOI":"10.1002\/cta.3046","article-title":"A true random number generator that utilizes thermal noise in a programmable system-on-chip (PSoC)","volume":"49","author":"Matsuoka","year":"2021","journal-title":"Int. J. Circuit Theory Appl."},{"key":"ref_9","unstructured":"Franco Moreno, J.J., Alsina Pag\u00e8s, R.M., and V\u00e1zquez Alcocer, P.P. (2022, January 19\u201322). Visual analysis of environmental noise data. 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