Algorithmic Decomposition of Geometric Islamic Patterns: A Case Study with Star Polygon Design in the Tombstones of Ahlat

  • Asli AgirbasEmail author


The current practice is to make the mathematical analysis of many Islamic patterns in 2D; however, since such patterns actually have 3D features, the third dimension must also be considered. Indeed, the three-dimensional features of the patterns made by carving on stone are very numerous. In this work, it is proposed to perform a 3D mathematical analysis of patterns of this type by algorithmic decomposition. In the cemetery of Ahlat, which is an existing monument, a tombstone with high three-dimensional features, designed by Asil b. Veys (Uveys), was chosen for algorithmical analysis. The mathematical design rules of the star polygon pattern in the selected monument were determined, as based on the shape grammar theory. The probable rules for the creation of the star polygon pattern in this study were produced simultaneously in the computer environment using a visual programming language and a 3D parametric pattern generator of the pattern was created.


Design analysis Geometric islamic patterns Shape grammars Design computation Parametric design 


  1. Alacam, S., Guzelci O.Z., Gurer, E. and S.Z. Bacinoglu. 2017. Reconnoitring computational potentials of the vault-like forms: Thinking aloud on muqarnas tectonics. International Journal of Architectural Computing 15 (4): 285–303.CrossRefGoogle Scholar
  2. Arik, M. and M. Sancak. 2007. Turkish-Islamic Art and Penrose Tilings. Balkan Physics Letters 15 (3): 84–95.Google Scholar
  3. Baykara, T. and M.C. Isik. 2016. Physical Characterization, Microstructural Evaluation, and Condition Assessment of Ancient Ahlat Tombstones in the Seljukian Cemetery of Ahlat (Turkey). International Journal of Architectural Heritage 10 (8): 1025–1040.CrossRefGoogle Scholar
  4. Beatini, V. 2017. Kinetic Rosette Patterns and Tessellations. International Journal of Computational Methods and Experimental Measurements 5 (4): 631–641.CrossRefGoogle Scholar
  5. Bodner, B.L. 2012. From Sultaniyeh to Tashkent Scrolls: Euclidean Constructions of Two Nine- and Twelve-Pointed Interlocking Star Polygon Designs. Nexus Network Journal 14 (2): 307–332.CrossRefGoogle Scholar
  6. Bonner, J. 2003. Three traditions of self-similarity in fourteenth and fifteenth century Islamic geometric ornament. In: ISAMA-BRIDGES Conference Proceedings (Granada, Spain, July 23-25), eds. J. Barrallo, J. Martinez-Aroza, N. Friedman, R. Sarhangi, J.A. Maldonado and C. Sequin, 1–12. Accessed 3 August 2018.
  7. Bonner, J.F. 2016. The Historical Significance of the Geometric Designs in the Northeast Dome Chamber of the Friday Mosque at Isfahan. Nexus Network Journal 18: 55–103.CrossRefGoogle Scholar
  8. Bonner, J. 2017. Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction. NY: Springer.CrossRefGoogle Scholar
  9. Bourgoin, J. 1879. Les Eléments de l’Art Arabe: Le Trait des Entrelacs. Paris: Firmin-Didot.Google Scholar
  10. Broug, E. 2008. Islamic Geometric Patterns. London: Thames and Hudson.Google Scholar
  11. Burckhardt, T. 2009. Art of Islam: Language and Meaning. Bloomington, Indiana: World Wisdom Inc.Google Scholar
  12. Castera, Jean-Marc. 2011. Flying Patterns. In: Bridges Coimbra Conference Proceedings (Coimbra, Portugal, July 27-31), eds. R. Sarhangi and C. Sequin, 263–270. Phoenix, Arizona: Tessellations Publishing.Google Scholar
  13. Cenani, Sehnaz and Gulen Cagdas. 2007. A Shape Grammar Study: Form Generation with Geometric Islamic Patterns. In: 10th Generative Art Conference Proceedings (Milan, Italy, December 12–14), ed. C. Soddu, 216–223. Milan: Domus Argenia Publisher.Google Scholar
  14. Corcuff, Marie-Pascale. 2018. Jules Bourgoin (1838–1908): A Forerunner of Generative Shape Grammers. In: Nexus Architecture and Mathematics 2018 Conference Book, eds. Kim Williams and Marco Giorgio Bevilacqua, 257–262. Kim Williams Books.Google Scholar
  15. Critchlow, K. 1983. Islamic Patterns: An Analytical and Cosmological Approach. London: Thames & Hudson.Google Scholar
  16. Cromwell, P.R. 2009. The Search for Quasi-Periodicity in Islamic 5-fold Ornament. The Mathematical Intelligencer 31: 36–56.MathSciNetCrossRefGoogle Scholar
  17. Demiriz, Y. 2000. Islam sanatinda Geometrik susleme: Bir Envanter Denemesi. Istanbul: Lebib Yalkin Yayinlari.Google Scholar
  18. Duarte, J.P. 2005. Towards the mass customization of housing: the grammar of Siza’s houses at Malagueira. Environment and Planning B: Planning and Design 32 (3): 347–380.CrossRefGoogle Scholar
  19. El-Said, I. and A. Parman. 1976. Geometric Concepts in Islamic Art. London: World of Islam Festival Publishing Company Ltd.Google Scholar
  20. Hankin E.H. 1925a. The Drawing of Geometric Patterns in Saracenic Art. Archaeological survey of India: Memoirs. Calcutta: Government of India, Central Publication Branch.Google Scholar
  21. Hankin E.H. 1925b. Examples of methods of drawing geometrical arabesque patterns. The Mathematical Gazette 12: 371–373.CrossRefGoogle Scholar
  22. Isik, E., Bakis, A., Akilli, A. and F. Hattatoglu. 2015. Usability of Ahlat Stone as Aggregate in Reactive Powder Concrete. Int. Journal of Applied Sciences and Engineering Research 4 (4): 507–514.Google Scholar
  23. Kaplan, C.S. and D.H. Salesin. 2004. Islamic Star Patterns in Absolute Geometry. ACM Transactions on Graphics 23 (2): 97–119.CrossRefGoogle Scholar
  24. Kaplan, C.S. 2005. Islamic Star Patterns from Polygons in Contact. In: Proceedings of the Graphics Interface 2005 Conference (May 9-11, Victoria, British Columbia, Canada), ed. M. McCool, 177–185. Waterloo, Ontario: Canadian Human-Computer Communications Society and A K Peters Ltd.Google Scholar
  25. Karamagarali, B.1992. Ahlat Mezar Taslari. Ankara: Kultur Bakanligi Yayinlari.Google Scholar
  26. Kasraei, M.H., Nourian, Y. and M. Mahdavinejad, 2016. Girih for domes: analysis of three Iranian domes. Nexus Network Journal 18: 311–321.CrossRefGoogle Scholar
  27. Knight, T. and G. Stiny. 2015. Making grammars: From computing with shapes to computing with things. Design Studies 41: 8–28.CrossRefGoogle Scholar
  28. Kuban, D. 2002. Selcuklu Caginda Anadolu Sanati. Istanbul: Yapi Kredi Yayinlari.Google Scholar
  29. Makovicky, E. and N.M. Makovicky. 2017. Nonperiodic Octagonal Patterns from a Jali Screen in the Mausoleum of Muhammad Ghaus in Gwalior and Their Periodic Relatives. Nexus Network Journal 19: 101–120.CrossRefGoogle Scholar
  30. Mulayim, S. 1982. Anadolu Turk Mimarisinde Geometrik Suslemeler: Selcuklu Cagi. Ankara: Kultur ve Turizm Bakanligi Yayinlari.Google Scholar
  31. Necipoglu, G. 1995. The Topkapi Scroll- Geometry and Ornament in Islamic Architecture: Topkapi Palace Museum Library MS H. Santa Monica, CA: The Getty Center for the History of Art and the Humanities.Google Scholar
  32. Oney, G. 1978. Anadolu Selcuklu Mimarisinde Susleme ve El Sanatlari. Ankara: Turkiye Is Bankasi Kultur Yayinlari.Google Scholar
  33. Ozkar, M. 2011. Visual schemas: pragmatics of design learning in foundations studios. Nexus Network Journal 13 (1): 113–130.CrossRefGoogle Scholar
  34. Redondo-Buitrago, A. and D. Huylebrouck. 2015. Nonagons in the Hagia Sophia and the Selimiye Mosque. Nexus Network Journal 17 (1): 157–181.CrossRefGoogle Scholar
  35. Redondo-Buitrago, Antonia. 2018. On Polygons, Set Squares and Mudejar Carpentry. In: Nexus Architecture and Mathematics 2018 Conference Book, eds. Kim Williams and Marco Giorgio Bevilacqua, 73–77. Kim Williams Books.Google Scholar
  36. Rigby, J. 2005. A Turkish Interlacing Pattern and the Golden Ratio: Whirling Dervishes and a Geometry Lecture in Konya. Mathematics in School 34 (1): 16–24.Google Scholar
  37. Sarhangi, R. 2012. Interlocking Star Polygons in Persian Architecture: The Special Case of the Decagram in Mosaic Designs. Nexus Network Journal 14 (2): 345-372.CrossRefGoogle Scholar
  38. Schneider, 1980. Geometrische Bauornamente der Seldschuken in Kleinasien. Wiesbaden: Reichert.Google Scholar
  39. Stiny, G. and J. Gips. 1972. Shape grammars and the generative specification of painting and sculpture. Information Processing 71: 1460–1465.Google Scholar
  40. Stiny, G. 2006. Shape: Talking about Seeing and Doing. Cambridge, Massachusetts: MIT Press.Google Scholar
  41. Wilson, E. 1988. Islamic Designs. London: The British Museum Press.Google Scholar

Copyright information

© Kim Williams Books, Turin 2018

Authors and Affiliations

  1. 1.Department of ArchitectureFatih Sultan Mehmet Vakif UniversityIstanbulTurkey

Personalised recommendations