The Monthly Scientific Journal of Bagh-e Nazar

Analysis of Fractal Geometry in the Maqeli Tiled Spandrel of the Northern Iwan in Hakim Mosque in Isfahan

https://doi.org/10.22034/bagh.2024.442928.5562
Volume 21, Issue 135
September 2024
Pages 51-62
The Monthly Scientific Journal of Bagh-e Nazar

Document Type : Original Research Article

Authors

Keyhaneh Reisi 1
Iman Zakariaee 2
Jalil Jokar 3
Samad Najarpoor 4

1 Master’s student in Persian Painting,Caligraphy Department, The Faculty of Handicrafts, Isfahan University of Art, Iran.

2 Associate Professor, Carpet Studies Department, The Faculty of Handicrafts, Isfahan University of Art, Iran.

3 3. Instructor,Islamic Art Department, The Faculty of Handicrafts, Isfahan University of Art, Iran.

4 Assistant Professor, Caligraphy Department, The Faculty of Handicrafts, Isfahan University of Art, Iran.

Abstract
Problem statement: Geometric knots are prevalent patterns in Islamic architectural designs characterized by complexity, Plurality, rhythm, and balance in drawing, extending beyond Euclidean geometry. Fractal geometry as a foundation of forming the universe and nature is non-Euclidean. Many artists, besides knowing geometry, use nature as a model, thus creating their artwork perhaps unconsciously or consciously based on fractal geometry. One of these enduring manifestations is the Hakim Mosque in Isfahan. Since behind these beautiful works, there are hidden rules, and knowing these rules elevates our understanding to achieve beauty, the study of fractal geometry in these works reveals their hidden angles and beauty. This research seeks to answer the question: How can fractal geometry be used to analyze the geometric structure of the Maqeli tiled spandrel of the northern Iwan in Hakim Mosque?
Research objective: This research attempts to analyze the fractal geometry system in the Maqeli tiled spandrel of the northern Iwan in Hakim Mosque.
Research method: This research is applied in nature, utilizing field data collection, library and internet sources. The methodology is descriptive and analytical. It is noteworthy that the analysis of the knot dimensions was conducted using software. 
Conclusion: By analyzing the Maqeli patterns from a fractal perspective (self-similarity and dimension), the result of the research was the dimensions of these geometric patterns were fractional. These dimensions, calculated using two methods (logarithmic box-counting and software), showed minor differences and completely matched fractal dimensions. Furthermore, by linearizing the patterns with AutoCAD software and examining the hidden geometry, self-similarity, and repetition in the secret geometry of the designs as well as in the geometric patterns of the Maqeli tiles were revealed.

Keywords

Fractal geometry
Geometric Patterns
Fractional dimension
Self-similarity
Maqeli Tile
Hakim Mosque
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