Abstract
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.
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References
Al Ajlouni R (2011) A long-range hierarchical clustering model for constructing perfect quasicrystalline formations. Philos Mag 91:2728–2738
Al Ajlouni R (2012) The global long-range order of quasiperiodic patterns in Islamic architecture. Acta Crystallogr, Ser A 68:235–243
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
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.
El-Said E (1993) Islamic art and architecture: the system of geometric design. Garnet, Reading
Gonzalez V (2001) Beauty and Islam: aesthetic in Islamic art and architecture. Islamic Publications, London
Grünbaum B, Shephard GC (1986) Tilings and patterns. Freeman, New York
Kritchlow K (1976) Islamic patterns: an analytical and cosmological approach. Thames & Hudson, New York
Lu P, Steinhardt P (2007) Decagonal and quasicrystalline tilings in Medieval Islamic architecture. Science 315:1106–1110
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
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
Makovicky E, Makovicky N (2011) The first find of dodecagonal quasiperiodic tiling in historical Islamic architecture. J Appl Crystallogr 44:569–573
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
Penrose R (1974) The role of aesthetics in pure and applied mathematical research. Bull Inst Math Appl 10:266–271
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Al Ajlouni, R. (2013). Octagon-Based Quasicrystalline Formations in Islamic Architecture. In: Schmid, S., Withers, R., Lifshitz, R. (eds) Aperiodic Crystals. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6431-6_7
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DOI: https://doi.org/10.1007/978-94-007-6431-6_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-6430-9
Online ISBN: 978-94-007-6431-6
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