{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T18:49:04Z","timestamp":1779389344710,"version":"3.53.1"},"reference-count":26,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2018,8,9]],"date-time":"2018-08-09T00:00:00Z","timestamp":1533772800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. Comput. Cult. Herit."],"published-print":{"date-parts":[[2018,9,5]]},"abstract":"<jats:p>The discovery of quasi-crystals has led to a great debate about their unusual structure. The big surprise is that these structures were found in Islamic art several centuries ago. This latest discovery drew the attention of scientists to propose several approaches for the comprehension of these structures by analyzing several quasi-periodic patterns spread around the Islamic world. In this article, we propose a systematic method for generating new quasi-periodic patterns inspired by existing Islamic historical patterns. The method builds Islamic quasi-periodic patterns based on a quasi-periodic tiling and a few intuitive parameters. Given a quasi-periodic tiling, the method divides its tiles (rhombs) into symmetric right triangles and constructs their template motifs. The construction of these template motifs is achieved by a systematic and well-organized process. The content of the tiles is obtained by applying mirror reflections to the constructed template motifs. Finally, the pattern is drawn by putting the content of the constructed tiles in the tiling. To show the effectiveness of this generative method, examples of new quasi-periodic patterns will be presented.<\/jats:p>","DOI":"10.1145\/3127090","type":"journal-article","created":{"date-parts":[[2018,8,13]],"date-time":"2018-08-13T12:29:41Z","timestamp":1534163381000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["Generating Islamic Quasi-Periodic Patterns"],"prefix":"10.1145","volume":"11","author":[{"given":"Aziz","family":"Khamjane","sequence":"first","affiliation":[{"name":"Universit\u00e9 Sidi Mohamed Ben Abdellah, Fes, Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rachid","family":"Benslimane","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Sidi Mohamed Ben Abdellah, Fes, Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2018,8,9]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1107\/S1600576714001691"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/14786435.2010.532515"},{"key":"e_1_2_1_3_1","volume-title":"Octagon-Based Quasicrystalline Formations in Islamic Architecture","author":"Ajlouni Rima Al","unstructured":"Rima Al Ajlouni . 2013. Octagon-Based Quasicrystalline Formations in Islamic Architecture . Springer Netherlands , Dordrecht , 49--57. Rima Al Ajlouni. 2013. Octagon-Based Quasicrystalline Formations in Islamic Architecture. Springer Netherlands, Dordrecht, 49--57."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1107\/S010876731104774X"},{"key":"e_1_2_1_5_1","volume-title":"Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings, J. Barrallo et al. (Eds.)","author":"Bonner Jay","year":"2003","unstructured":"Jay Bonner . 2003 . Three traditions of self-similarity in fourteenth and fifteenth century Islamic geometric ornament . In Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings, J. Barrallo et al. (Eds.) . University of Granada, Granada, Spain, 1--12. Jay Bonner. 2003. Three traditions of self-similarity in fourteenth and fifteenth century Islamic geometric ornament. In Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings, J. Barrallo et al. (Eds.). University of Granada, Granada, Spain, 1--12."},{"key":"e_1_2_1_6_1","first-page":"99","article-title":"Zellijs, muqarnas and quasicrystals","volume":"99","author":"Castera Jean-Marc","year":"1999","unstructured":"Jean-Marc Castera . 1999 . Zellijs, muqarnas and quasicrystals . ISAMA 99 (1999), 99 -- 104 . Jean-Marc Castera. 1999. Zellijs, muqarnas and quasicrystals. ISAMA 99 (1999), 99--104.","journal-title":"ISAMA"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/1385-7258(81)90017-2"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/1385-7258(81)90016-0"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.54.2688"},{"key":"e_1_2_1_10_1","first-page":"1","article-title":"Mirador de lindaraja: Islamic ornamental patterns based on quasi-periodic octagonal lattices in Alhambra, Granada and Alcazar, Sevilla","volume":"19","author":"Makovicky Emil","year":"1996","unstructured":"Emil Makovicky and Fenoll Hach-Al\u00ed . 1996 . Mirador de lindaraja: Islamic ornamental patterns based on quasi-periodic octagonal lattices in Alhambra, Granada and Alcazar, Sevilla , Spain. Boletin De La Sociedad Espanola De Mineralogia 19 (1996), 1 -- 26 . Emil Makovicky and Fenoll Hach-Al\u00ed. 1996. Mirador de lindaraja: Islamic ornamental patterns based on quasi-periodic octagonal lattices in Alhambra, Granada and Alcazar, Sevilla, Spain. Boletin De La Sociedad Espanola De Mineralogia 19 (1996), 1--26.","journal-title":"Spain. Boletin De La Sociedad Espanola De Mineralogia"},{"key":"e_1_2_1_11_1","volume-title":"Computer generated Islamic star patterns. Bridges","author":"Kaplan Craig S.","year":"2000","unstructured":"Craig S. Kaplan . 2000. Computer generated Islamic star patterns. Bridges ( 2000 ), 105--112. Retrieved from http:\/\/www.cgl.uwaterloo.ca\/. Craig S. Kaplan. 2000. Computer generated Islamic star patterns. Bridges (2000), 105--112. Retrieved from http:\/\/www.cgl.uwaterloo.ca\/."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/990002.990003"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.2307\/1523103"},{"key":"e_1_2_1_15_1","volume-title":"Steinhardt","author":"Lu Peter J.","year":"2007","unstructured":"Peter J. Lu and Paul J . Steinhardt . 2007 . Decagonal and quasi-crystalline tilings in medieval islamic architecture. Science 315, 5815 (2007), 1106--1110. Peter J. Lu and Paul J. Steinhardt. 2007. Decagonal and quasi-crystalline tilings in medieval islamic architecture. Science 315, 5815 (2007), 1106--1110."},{"key":"e_1_2_1_16_1","volume-title":"Fivefold Symmetry","author":"Makovicky Emil","unstructured":"Emil Makovicky . 1992. 800-year-old pentagonal tiling from Maragha, Iran, and the new varieties of aperiodic tiling it inspired . In Fivefold Symmetry . World Scientific Publishing , Singapore , 67--86. Emil Makovicky. 1992. 800-year-old pentagonal tiling from Maragha, Iran, and the new varieties of aperiodic tiling it inspired. In Fivefold Symmetry. World Scientific Publishing, Singapore, 67--86."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1146262"},{"key":"e_1_2_1_18_1","first-page":"421","article-title":"In the footsteps of Maragha: Ornamental panels in the Madrasas and mosques of Esfahan, Konya","volume":"26","author":"Makovicky Emil","year":"2015","unstructured":"Emil Makovicky . 2015 . In the footsteps of Maragha: Ornamental panels in the Madrasas and mosques of Esfahan, Konya , Agra, Sivas and Yazd. Symmetry: Culture and Science 26 (2015), 421 -- 441 . Emil Makovicky. 2015. In the footsteps of Maragha: Ornamental panels in the Madrasas and mosques of Esfahan, Konya, Agra, Sivas and Yazd. Symmetry: Culture and Science 26 (2015), 421--441.","journal-title":"Agra, Sivas and Yazd. Symmetry: Culture and Science"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1107\/S0021889811013744"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00004-016-0316-6"},{"key":"e_1_2_1_21_1","first-page":"107","article-title":"Decagonal patterns in the Islamic ornamental art of Spain and Morocco","volume":"21","author":"Makovicky Emil","year":"1998","unstructured":"Emil Makovicky , Fernando Rull P\u00e9rez , and P. Fenoll Hach-Al\u00ed . 1998 . Decagonal patterns in the Islamic ornamental art of Spain and Morocco . Boletin de la Sociedad Espanola de Mineralogia 21 (1998), 107 -- 127 . Emil Makovicky, Fernando Rull P\u00e9rez, and P. Fenoll Hach-Al\u00ed. 1998. Decagonal patterns in the Islamic ornamental art of Spain and Morocco. Boletin de la Sociedad Espanola de Mineralogia 21 (1998), 107--127.","journal-title":"Boletin de la Sociedad Espanola de Mineralogia"},{"key":"e_1_2_1_22_1","first-page":"16","article-title":"Pentaplexity","volume":"39","author":"Penrose Roger","year":"1978","unstructured":"Roger Penrose . 1978 . Pentaplexity . Eureka 39 , 39 (1978), 16 -- 22 . Roger Penrose. 1978. Pentaplexity. Eureka 39, 39 (1978), 16--22.","journal-title":"Eureka"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF03024384"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.52842\/conf.acadia.2012.391"},{"key":"e_1_2_1_25_1","volume-title":"Architecture and Mathematics from Antiquity to the Future, Kim Williams and Michael J","author":"Saltzman Peter","unstructured":"Peter Saltzman . 2015. Quasi-periodicity in islamic geometric design . In Architecture and Mathematics from Antiquity to the Future, Kim Williams and Michael J . Ostwald (Eds.). Springer International Publishing , 585--602. Retrieved from http:\/\/link.springer.com\/chapter\/10.1007\/978-3-319-00137-1 Peter Saltzman. 2015. Quasi-periodicity in islamic geometric design. In Architecture and Mathematics from Antiquity to the Future, Kim Williams and Michael J. Ostwald (Eds.). Springer International Publishing, 585--602. Retrieved from http:\/\/link.springer.com\/chapter\/10.1007\/978-3-319-00137-1"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.53.1951"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.32.5547"}],"container-title":["Journal on Computing and Cultural Heritage"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3127090","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3127090","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T02:11:07Z","timestamp":1750212667000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3127090"}},"subtitle":["A New Method"],"short-title":[],"issued":{"date-parts":[[2018,8,9]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,9,5]]}},"alternative-id":["10.1145\/3127090"],"URL":"https:\/\/doi.org\/10.1145\/3127090","relation":{},"ISSN":["1556-4673","1556-4711"],"issn-type":[{"value":"1556-4673","type":"print"},{"value":"1556-4711","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,9]]},"assertion":[{"value":"2017-01-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-06-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-08-09","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}