Octagon-Based Quasicrystalline Formations in Islamic Architecture

  • Rima Al AjlouniEmail author


The unexpected discovery of ancient Islamic ornaments with quasicrystalline symmetries has triggered significant discussion and a number of debates on the mathematical sophistication of Islamic geometry and its generating principles. Astonishingly, eight centuries before its description in Modern Science, ancient artists had constructed patterns with perfect quasicrystalline formations. Recent studies have provided enough evidence to suggest that ancient designers, by using the most primitive tools (a compass and a straight edge), were able to resolve the complicated long-range principles of quasicrystalline formations. Derived from these principles, a global multi-level structural model is presented that is able to describe the global long-range order of octagon-based quasicrystalline formations in Islamic Architecture. This new method can be used as a general guiding principle for constructing infinite patches of octagon-based quasicrystalline formations, including Ammann–Beenker tiling, without the need for local strategies (matching, scaling, etc.) or complicated mathematics.


  1. 1.
    Al Ajlouni R (2011) A long-range hierarchical clustering model for constructing perfect quasicrystalline formations. Philos Mag 91:2728–2738 CrossRefGoogle Scholar
  2. 2.
    Al Ajlouni R (2012) The global long-range order of quasiperiodic patterns in Islamic architecture. Acta Crystallogr, Ser A 68:235–243 CrossRefGoogle Scholar
  3. 3.
    Al Ajlouni R (2012) The forbidden symmetries. In: Cabrinha M, Kelly J, Steinfeld K (eds) Synthetic digital ecologies. Acadia, San Francisco, pp 391–400. ISBN: 978-1-62407-267-3 Google Scholar
  4. 4.
    Bonner J (2003) Three traditions of self-similarity in fourteenth and fifteenth century Islamic geometric ornament. In: Sarhangi R, Friedman N (eds) Mathematical connections in art, music and science. Proceedings ISAMA/bridges. University of Granada, Granada pp 1–12. Google Scholar
  5. 5.
    El-Said E (1993) Islamic art and architecture: the system of geometric design. Garnet, Reading Google Scholar
  6. 6.
    Gonzalez V (2001) Beauty and Islam: aesthetic in Islamic art and architecture. Islamic Publications, London Google Scholar
  7. 7.
    Grünbaum B, Shephard GC (1986) Tilings and patterns. Freeman, New York Google Scholar
  8. 8.
    Kritchlow K (1976) Islamic patterns: an analytical and cosmological approach. Thames & Hudson, New York Google Scholar
  9. 9.
    Lu P, Steinhardt P (2007) Decagonal and quasicrystalline tilings in Medieval Islamic architecture. Science 315:1106–1110 CrossRefGoogle Scholar
  10. 10.
    Makovicky E (1992) 800-year-old pentagonal tiling from Maragha, Iran, and the new varieties of aperiodic tiling it inspired. In: Hargittai I (ed) Fivefold symmetry. World Scientific, Singapore, pp 67–86 Google Scholar
  11. 11.
    Makovicky E, Fenoll Hach-Ali P (1996) Mirador de Lindaraja: Islamic ornamental patterns based on quasiperiodic octagonal lattices in Alhambra, Granada, and Alcazar, Sevilla, Spain. Bol Soc Esp Mineral 19:1–26 Google Scholar
  12. 12.
    Makovicky E, Makovicky N (2011) The first find of dodecagonal quasiperiodic tiling in historical Islamic architecture. J Appl Crystallogr 44:569–573 CrossRefGoogle Scholar
  13. 13.
    Makovicky E, Rull Pérez F, Fenoll Hach-Alí P (1998) Decagonal patterns in the Islamic ornamental art of Spain and Morocco. Bol Soc Esp Mineral 21:107–127 Google Scholar
  14. 14.
    Penrose R (1974) The role of aesthetics in pure and applied mathematical research. Bull Inst Math Appl 10:266–271 Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.College of ArchitectureTexas Tech UniversityLubbockUSA

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