Abstract
The historical written sources introduced Vāgireh, a repeating unit, as the smallest constituent of Girih to make interlaced patterns. However, recent studies have shown that the smallest unit of Girih is a fundamental domain (fundamental domain which is the minimal repetitive design element that is needed to construct the whole pattern using one or combination of rotation, reflection or glide reflection). The Girih in the Blue Mosque of Tabriz in Iran are essential evidence of the relation between the fundamental domain and the Girih's formation. This study seeks to investigate the relationship between the formation of Girih with symmetries and awareness of the responsible artist in the Blue Mosque. This research shows that Girih have different levels of repetition, and the final product of the pattern does not only depend on the fundamental domain; it also relates to its applied symmetry. The responsible artist of the Girih on the Blue Mosque plinth had knowledge of the repetitive principles and could present different patterns from the same unit which is called a fundamental domain nowadays.
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Notes
Persian sources introduce the motif as Alāt; Hence, in this article, the word motif refers to Alāt.
Examples of these scrolls include Topkapi, Fī tadākhul al-ashkāl al-mutashābiha aw al-mutawāfiqa (ﻓﻲ ﺗﺪاﺧﻞ اﻷﺷﮑﺎل اﻟﻤﺘﺸﺎﺑﻬﺔ أو اﻟﻤﺘﻮاﻓﻘﺔ/A Persian Compendium on Similar and Complementary Interlocking Figures), and Mirza Ali-Akbar (میرزا علی اکبر).
In Persian sources, the repeating unit is referred to as Vāgireh; throughout the article repeating units refers to Vāgireh.
‘The fundamental domain is the smallest component that is essential for design repetition (Bonner 2017: 156).
Abu Nasr Muhammad Al-Farabi (Kitab al-musiqa al-kabir).
Abū-ʿAlī al-Ḥusayn ibn-ʿAbdallāh Ibn-Sīnā (Book: Kitab al-Najah (Ghesm al-mosiqi)).
Safi al-Din al-Urmawi al-Baghdadi (Book: Kitāb al-advār fi al-musiqā).
Abd al- Qadir b. GHaybi al-Hafiz al-Maraghi (Book: Kitāb Jameh al-alhan).
The Turkmen period included the Qaraqoyunlu and Aq Qoyunlu dynasties; the Blue Mosque was built during the Aq Quyunlu period.
Hiyal (حیل/الحیل) is a subdivision of the science of construction during the Islamic period.
In the Persian source, the star is introduced as Shāmseh (شمسه); throughout the article, the word star refers to Shāmseh.
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Acknowledgements
The authors composed all figures in this paper unless stated otherwise. In addition, the authors would like to thank Dr. Siflo, professor of Tabriz University, and Mr.Sheikhol Hokamaei, professor of Tehran University, for their guidance in using the historical manuscripts.
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Appendix
Appendix
Zero-dimensional expansion The expansive elements are organized around a rotational symmetry revolving around a point. The pattern can have n-fold symmetries according to the number of the axes of symmetry (Makovicky 2016).
Template tiling/ underlying generative tessellation In the polygonal technique, a polygonal tessellation is used for generating geometric patterns. Pattern lines are placed upon key points of the polygonal edges, and after completing the pattern, the underlying polygonal tessellation is discarded. This is sometimes referred to as a sub-grid (Bonner 2017: 577).
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Shoubi, A.A., Ebrahimi, A.N. & Shahbazi, Y. Modularity and Symmetry in Girih: A Case Study of the Blue Mosque in Tabriz-Iran. Nexus Netw J (2023). https://doi.org/10.1007/s00004-023-00656-w
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DOI: https://doi.org/10.1007/s00004-023-00656-w