Comparative analysis of geometric forms and numerical calculation of fractals in Khayyam’s Mausoleum based on the Islamic architecture’s definitions and box-counting method

الموضوعات : Space Ontology International Journal

Hengame Rezazade ¹ (Department of Arts and Architecture ,Islamic Azad University, Yadegar-e- Imam Khomeini (RAH) Shar-e-Rey Branch, Tehran, Iran)
Mahta Tari ² (Department of Arts and Architecture ,Islamic Azad University, Yadegar-e- Imam Khomeini (RAH) Shar-e-Rey Branch, Tehran, Iran)

تاريخ الإرسال : 25 الأربعاء , ربيع الأول, 1442 تاريخ التأكيد : 07 الأربعاء , ربيع الأول, 1443 تاريخ الإصدار : 26 الأربعاء , ربيع الثاني, 1443

الکلمات المفتاحية: Fractal geometry, fractal dimension, Box-counting, Fractal’s application, Khayyam’s Mausoleum,

ملخص المقالة :

The interaction and balance between fractal components, which maintain to function in nature in perfect harmony with the highest efficiency, has been the source of inspiration for architects in different eras. Today, contemporary Iranian architecture needs a comprehensive study and familiarity with world issues, hence the Khayyam’s mausoleum was chosen. the main purpose of this article is to analyze the geometry and numerical calculation of the fractal size of the building and its semantic knowledge in the contemporary building, which leads to finding the architect’s goals of how to design these forms and common concepts with Islamic architecture. After achieving how to use Islamic elements in a contemporary monument, we come to the interrelationship between fractal geometry and architectural design.With the box-counting technique, the fractal dimension was calculated by checking the two-dimensional plates in 4 different scales from the largest to the smallest scale to prove its decimal dimension. Then, information was collected by descriptive-analytic method and after determining the common features between fractal forms with analytical and comparative process, the obtained quantitative data resulted in extracting similar cases from the building. Finally, the relationship between the characteristics of fractal geometry and the architecture of the tomb was proved and the obtained patterns were matched with the concepts of self-similarity, iteration (proportion and symmetry), micro scale and non-integer dimension. The elements used such as tiled ornaments, the Islamic star and Shamsa, domed-shaped roof, regular numerical pattern of geometric shapes with symbolism, unity in diversity, infinity and dynamism are reminiscent of Islamic architectural style. Furthermore, fractal has been used in three methods: conceptual, mathematical and intuitive, and has been manifested in both structural and aesthetic aspects.

المصادر:

1. Abdelsalam, M., & Ibrahim, M. (2019). Fractal dimension of Islamic Architecture: The case of the Mameluke Madrasas: Al-sultan Hassan Madrasa, Journal of Science Gazi University. 32 (1). 27-37.


2. Abedi, M.  & Ebrahimi, H. (2015). Typology of Iranian architectural tomb buildings. National conference of native architecture and urbanism of Iran. February, (pp. 1-10). Yazd.


3. Alik, B. (2015). Mimarlik tasarlama yontemleri ve fractal tasarimlar uzerine bir inceleme (A study on design methods and fractal design in architecture). Master Thesis, Kocaeli University, Institute of Applied Science, Faculty of architecture and design, Kocaeli, Turkey (in Turkish).


4. Alik, B., & Ayyildiz, S. (2016). Fractal and fractal design in architecture. 13^th international conference “standardization, prototypes and quality: A means of Balkan countries’ collaboration”. November 3-4, (PP. 282-291). Romania: Transilvania University of Brasov.


5. Ardalan, N., & Bakhtiar, L. (2005). The sense of unity. Isfahan: Khak publications.


6. Bovill, C. (1996). Fractal Geometry in Architecture and design. Boston: Birkhauser.


7. Broug, E. (2008). Islamic Geometric patterns. London: Thames and Hudson Ltd.


8. Cooper. J. C. (2007). An illustrated encyclopedia of traditional symbols. (Malihe, Karbasian, Trans.), Tehran: Nashrenow publications.


9. Delkhosh, M. (2017). Introduction of fractals and fractional dimensions. Math and society Journal, 2 (1), 1- 23.


10. Elgohari, A. (2019). The Transformation of Using Fractal Forms between Islamic and Digital Architecture from a Sustainable Approach (Case study: King Abdullah Petroleum Studies & research center, Riyadh, K.S.A), The Academic Research Community Publication. 3 (3), 87-98. DOI:10.21625/Archive.v3i3.526.


11. Hillenbrand. R. (2001). Islamic Architecture: Form, Function and Meaning. (Bagher, Ayatollahzadeh Shirazi, Trans.). Tehran: Rowzanehnashr Publications.


12. Ghaseminia, M., & Soltanzadeh, H. (2016). Intertextual Relationships in the Contemporary Architecture of Iran during 1961-1977. Space Ontology International Journal, 5 (4), 39-50.


13. Jiang, Sh., & Liu, D. (2012). Box counting dimension of fractal urban form: stability issues and measurement design. International Journal of Artificial life Research, 3(3), 41-63.


14. Khajvand Jafari, F.; Asgari, M.; &Pishkoo, M. (2019). The fractal calculus for materials. Journal of fractal and fractional, 3(8), 1-8.


15. Kholladi, M. (2004). Fractal structure of the urban objects. International Arab journal of information technology, 1(2), 164-170.


16. Li, J.; Du, Q; & Sun, C. (2009). An improved box-counting method for image fractal dimension estimation. Pattern recognition, 42(11), 2460-2469. DOI: 10.1016/j.PATCOG.2009.03.001.


17. Madadpour, M. (1995). The manifestation of spiritual wisdom in Islamic art, Tehran: International publishing co.


18. Mandelbrot, B. (1985). Self-Affine Fractals and Fractal Dimension. Phys. Scr, 32(4), 257. DOI: https;//doi.org/10.1088/0031-8949/32/4/001.


19. Mujdehi. M. (2016). World-Class architecture in the Iranian style from the point of view of experts, Tehran: Noandishan online publications.


20. Nurujjaman, Md.; Hossain, A.; & Ahmed, P. (2017). A review of fractal properties: mathematical approach. Science Journal of applied mathematics and statistics. 5(3), 98-105. DOI: 10.11648/J.SJAMS.20170503.11.


21. Osama, A.; Sherif, L; & Ezzeldin, Sh. (2014). Fractal geometry in architecture: from formative idea to superficial skin design. Archdesign Journal. Vol. 14, 39-49.


22. Parashar, R., & Bandyopadhyay, A. (2014). Fractals, Architecture and Sustainability.  Journal of Recent research in science and technology, 6(1),


23. Rumiez, A. (2013). Fractal architecture. Architecture and urban planning journal, Vol. 8, 45-49.


24. Sala, N. (2001). Fractal Models in Architecture: A Case of Study. Proceeding International Conference on “Mathematics for Living”, November 18-23, (pp. 266-272). Jordan.


25. Salingaros, N. A. (1999). Architectures, Patterns and Mathematics, Nexus Network Journal, Vol. 1, 77-85. DOI: http:// doi.org/10.1007/ s00004-998-0006-0.


26. Sarhangi, R. (1999). The sky within: mathematical aesthetics of Persian dome interiors. Nexus Network Journal, 1. DOI: 10.1007/s00004-998-0007-z.


27. Shishin. M. Y., & Aldeen Ismail, Kh. J. (2016). A method of compositional fractal analysis and its application in Islamic architectural Ensembles. International Electronic Journal of Mathematics Education, 11(5), 1087-1100.


28. Soheili, J. (2015). The Role of Nationalist leaders in Emergence of National Architectural Movements in Iran, 1924 to 1942. Space Ontology International Journal, 4 (13), 53-62.


29. Soltanzadeh, H. (2015). The role of climate and culture on the formation of courtyards in mosques. Space Ontology International Journal, 4 (3), 19-28.


30. Wu, J.; Jin, X.; Mi, Sh.; & Tang, J. (2020). An effective method to compute the box-counting dimension based on the mathematical definition and intervals. Results in Engineering, 6 (2020), 1-8.


31. Yahaqqi. M. J. (1996). A dictionary of myths and narrative symbols in Persian literature. Tehran: Soroush publications.