{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T16:52:36Z","timestamp":1776185556066,"version":"3.50.1"},"reference-count":69,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T00:00:00Z","timestamp":1559260800000},"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>Art is the output of a complex system based on the human spirit and driven by several inputs that embed social, cultural, economic and technological aspects of a given epoch. A solid quantitative analysis of art poses considerable difficulties and reaching assertive conclusions is a formidable challenge. In this paper, we adopt complexity indices, dimensionality-reduction and visualization techniques for studying the evolution of Escher\u2019s art. Grayscale versions of 457 artworks are analyzed by means of complexity indices and represented using the multidimensional scaling technique. The results are correlated with the distinct periods of Escher\u2019s artistic production. The time evolution of the complexity and the emergent patterns demonstrate the effectiveness of the approach for a quantitative characterization of art.<\/jats:p>","DOI":"10.3390\/e21060553","type":"journal-article","created":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:59:56Z","timestamp":1559303996000},"page":"553","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Complexity Analysis of Escher\u2019s Art"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio M.","family":"Lopes","sequence":"first","affiliation":[{"name":"UISPA\u2013LAETA\/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-4879","authenticated-orcid":false,"given":"J. A.","family":"Tenreiro Machado","sequence":"additional","affiliation":[{"name":"Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, R. Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4249-015 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,31]]},"reference":[{"key":"ref_1","unstructured":"Janson, H.W., and Janson, A.F. (2004). History of Art: The Western Tradition, Prentice Hall Professional."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Shiner, L. (2001). The Invention of Art: A Cultural History, University of Chicago Press.","DOI":"10.7208\/chicago\/9780226753416.001.0001"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cucker, F. (2013). Manifold Mirrors: The Crossing Paths of the Arts and Mathematics, Cambridge University Press.","DOI":"10.1017\/CBO9781139014632"},{"key":"ref_4","unstructured":"Russoli, F. (1962). 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