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Graph."],"published-print":{"date-parts":[[2021,6,30]]},"abstract":"<jats:p>\n            A fractal tiling (\n            <jats:italic>f<\/jats:italic>\n            -tiling) is a kind of rarely explored tiling by similar polygonal tiles which possesses self-similarity and the boundary of which is a fractal. Based on a tiling by similar isosceles right triangles, Dutch graphic artist M. C.\u00a0Escher created an ingenious print\n            <jats:italic>Square Limit<\/jats:italic>\n            in which fish are uniformly reduced in size as they approach the boundaries of the tiling. In this article, we present four families of\n            <jats:italic>f<\/jats:italic>\n            -tilings and propose an easy-to-implement method to achieve similar Escher-like drawings. By systematically investigating the local star-shaped structure of\n            <jats:italic>f<\/jats:italic>\n            -tilings, we first enumerate four families of\n            <jats:italic>f<\/jats:italic>\n            -tilings admitted by kite-shaped or dart-shaped prototiles. Then, we establish a fast binning algorithm for visualising\n            <jats:italic>f<\/jats:italic>\n            -tilings. To facilitate the creation of Escher-like drawings on the reported\n            <jats:italic>f<\/jats:italic>\n            -tilings, we next introduce one-to-one mappings between the square, and kite and dart, respectively. This treatment allows a pre-designed square template to be deformed into all prototiles considered in the article. Finally, we specify some technical implementations and present a gallery of the resulting Escher-like drawings. The method established in this article is thus able to generate a great variety of exotic Escher-like drawings.\n          <\/jats:p>","DOI":"10.1145\/3456298","type":"journal-article","created":{"date-parts":[[2021,7,15]],"date-time":"2021-07-15T19:43:39Z","timestamp":1626378219000},"page":"1-34","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":21,"title":["Self-Similar Fractal Drawings Inspired by M. C. Escher\u2019s Print\n            <i>Square Limit<\/i>"],"prefix":"10.1145","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0447-3190","authenticated-orcid":false,"given":"Peichang","family":"Ouyang","sequence":"first","affiliation":[{"name":"Guangxi University of Science and Technology, P.R. China and Jinggangshan University, P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kwok Wai","family":"Chung","sequence":"additional","affiliation":[{"name":"City University of Hong Kong, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alain","family":"Nicolas","sequence":"additional","affiliation":[{"name":"Nicolas Tessellation, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Krzysztof","family":"Gdawiec","sequence":"additional","affiliation":[{"name":"University of Silesia, Sosnowiec, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2021,7,15]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"M. A. Armstrong. 1988. Groups and Symmetry. Springer-Verlag New York.  M. A. Armstrong. 1988. Groups and Symmetry. Springer-Verlag New York.","DOI":"10.1007\/978-1-4757-4034-9"},{"key":"e_1_2_1_2_1","first-page":"549","article-title":"Self-similar sets 5. Integer matrices and fractal tilings of","volume":"112","author":"Bandt C.","year":"1991","unstructured":"C. Bandt . 1991 . Self-similar sets 5. Integer matrices and fractal tilings of . Proceedings of the American Mathematical Society 112 , 2 (1991), 549 \u2013 562 . DOI:https:\/\/doi.org\/10.2307\/2048752 10.2307\/2048752 C. Bandt. 1991. Self-similar sets 5. Integer matrices and fractal tilings of . Proceedings of the American Mathematical Society 112, 2 (1991), 549\u2013562. DOI:https:\/\/doi.org\/10.2307\/2048752","journal-title":"Proceedings of the American Mathematical Society"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.5555\/2408345"},{"key":"e_1_2_1_4_1","volume-title":"Retrieved on","author":"Bulatov V.","year":"2021","unstructured":"V. Bulatov . 2020. Hyperbolic Tilings . Retrieved on 18 February , 2021 from http:\/\/bulatov.org\/math\/index.html. V. Bulatov. 2020. Hyperbolic Tilings. 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Retrieved on 18 February, 2021 from https:\/\/mcescher.com\/lw-443\/."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0097-8493(00)00134-5"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0097-8493(02)00097-3"},{"key":"e_1_2_1_10_1","volume-title":"Bridges Conference, Southwestern College","author":"Fathauer R. W.","year":"2005","unstructured":"R. W. Fathauer . 2005 . Fractal tilings based on dissections of polyhexes. In Renaissance Banff: Mathematics, Music, Art, Culture, R. Sarhangi and R. V. Moody (Eds.) . Bridges Conference, Southwestern College , Winfield, Kansas, 427\u2013434. R. W. Fathauer. 2005. Fractal tilings based on dissections of polyhexes. In Renaissance Banff: Mathematics, Music, Art, Culture, R. Sarhangi and R. V. Moody (Eds.). Bridges Conference, Southwestern College, Winfield, Kansas, 427\u2013434."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1201\/9780429197123"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492914000129"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.4171\/JFG\/37"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1999.0268"},{"key":"e_1_2_1_15_1","unstructured":"B. Gr\u00fcnbaum and G. C. Shephard. 2016. Tilings and Patterns (2nd ed.). Dover Publications New York.  B. Gr\u00fcnbaum and G. C. Shephard. 2016. Tilings and Patterns (2nd ed.). Dover Publications New York."},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/1058129.1058131"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.3722\/cadaps.2009.737-748"},{"key":"e_1_2_1_19_1","volume-title":"Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture","author":"Kaplan C. S.","unstructured":"C. S. 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