روشی نو برای ترسیم نقوش تزئینی معماری اسلامی با استفاده از الگوی نگارال

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشیار، گروه معماری، دانشکده فنی و مهندسی، دانشگاه قم، قم، ایران.

2 دانشیار، گروه مهندسی کامپیوتر ، دانشکده فنی و مهندسی، دانشگاه قم، قم، ایران.

3 کارشناسی ارشد معماری، دانشکده معماری و شهرسازی، دانشگاه علم و صنعت، تهران، ایران.

چکیده

امروزه ارتباط گسترده میان هنر و علومی همچون ریاضیات و علم رایانه، امری غیرقابل انکار است. در همین راستا مطالعات میان رشته ای جهت برقراری تعامل میان دانش‌های مختلف با یکدیگر، به منظور تسهیل درک و فهم موضوعات از جنبه ها و ابعاد مختلف به میان می ‌آید. فرکتال (معادل فارسی برخال) از جمله این مباحث میان رشته ای است که رد پای آن در بسیاری از زمینه های علمی و هنری مشاهده می گردد. فرکتال‌ها برگرفته از طبیعت هستند، با هندسه و ریاضیات در ارتباط هستند و از قرن ها پیش در هنر و معماری سنتی و کلاسیک مورد استفاده قرار می‌گرفتند.
هدف از این پژوهش دستیابی و بازتولید الگوی هندسه فرکتالی به کار رفته در نقوش و گره های پرکاربرد معماری اسلامی و ترجمه آن به زبان نرم افزاری با بهره گیری از قوانین روش نگارال (L_system ) و به کمک زبان رایانه می باشد. از جمله‌ی مزایای حاصل از کاربست یافته های این پژوهش می توان به این موارد اشاره نمود: افزایش سرعت و کاهش چشم گیر خطا در روند طراحی نقوش هندسی معماری اسلامی و همچنین دستیابی به فرم ها و الگوهای نوین و پیچیده تر تنها با ایجاد تغییر های جزئی در داده های سیستم.

کلیدواژه‌ها


عنوان مقاله [English]

A New Approach to Drawing Decorative Motifs of Islamic Architecture Using L-system Pattern

نویسندگان [English]

  • Mohammad Mannan Raeesi 1
  • Yaghoub Farjami 2
  • Zeinab Ghasemi Sangi 3
1 Associate Professor, Department of Architecture, Faculty of Technology and Engineering, University of Qom, Qom, Iran.
2 Associate Professor, Department of Computer Engineering, Faculty of Engineering and Technology, University of Qom, Qom, Iran.
3 M.Sc. in Architecture, School of Architecture and Environmental Design, Iran University of Science and Technology (IUST), Tehran, Iran.
چکیده [English]

Traditional girih consists of basic geometric units with distinctive patterns, often built on repeated squares and circles. Early Islamic geometric forms—such as 8-pointed stars and lozenges—date back to 836 CE at the Great Mosque of Kairouan. By 1086, 7- and 10-point girih patterns appeared in the Jameh Mosque of Isfahan, and 10-point girih later became widespread. Girih designs are executed in cut brickwork, stucco, and mosaic faience tilework, forming decorative strapwork surfaces from the 15th to 20th centuries. Most designs rely on a hidden geometric grid with regular points, employing 2-, 3-, 4-, and 6-fold rotational symmetries to fill the plane. The visible pattern includes 10- and 12-pointed stars and convex polygons, joined by interlacing straps. This research uses a combinative method based on library documentation and mathematical logic. Comparing traditional and proposed methods, the new approach minimizes error coefficient and reduces time by eliminating the compass, the most sensitive drawing tool. The study aims to obtain and reproduce fractal geometry patterns from common Islamic girih motifs, translating them into software using L-system rules and computer language. It seeks to bridge architectural concepts with computational methods by examining fractal geometry in nature and architecture, redefining Islamic geometric patterns, and simulating them digitally. Benefits include significantly increased speed, reduced error in designing Islamic geometric patterns, and the ability to generate new, sophisticated forms through minor changes in system data.

کلیدواژه‌ها [English]

  • Fractal Geometry
  • Geometric Motifs
  • Islamic Architecture
  • L-system
Ayatollahi, Minou et al. (2018). Culture and Art. Iran Book Printing and Publishing Company Tehran.
Eftekharzadeh, Sanaz. (2013). From the Chaos of Perception to the Cognition of Architecture. Simaye
      ‌Danesh Publications, Tehran.
Bagheri, Vahideh and Babaei Eskoui, Solmaz. (2011). Digital Architecture and Its Impact on the
 ‌     Process of Architectural and Structural Design in Architects’ Projects. The Second International
 ‌     Conference on Architecture and Structure, University of Tehran, 1-10.
Becola, Sandra. (2008). The Art of Modernism. Translated by Rooin Pakbaz and Helia Darabi.
      ‌Farhang-e Moaser Publications, Tehran.
Balilan Asl, Lida et al. (2011). Investigation of the Geometrical Features of Knots in Islamic
       ‌Decorations from the Perspective of Fractal Geometry. Journal of Iranian-Islamic City Studies, 2(6),
      ‌83-95.
Bemanian, Mohammadreza; Amirkhani, Arian and Lilian, Mohammadreza. (2010). Order and
      ‌Disorder in Architecture. Tahan Publications, Tehran.
Tafaghodi Khajavi, Neda. (2016). Design of the International Convention Center of Mashhad Based
       ‌on Reflection on the Position of Fractal Geometry in Iranian Architecture. Master’s Thesis, Faculty
       ‌of Art and Architecture, Yazd University.
Jafari, Pedram. (2018). Negaral: A Method for Generating Fractals. Mathematics and Society Journal,
       ‌3(2), 59-68.
Rezalu, Reza; Airmelou, Yahya and Mirza Aghajani, Asadollah. (2012). Study of the Evolution of
       Cross Motifs in the Architectural Decorations of the Islamic Period of Iran and Their Aesthetic and
      ‌Symbolic Meanings. Fine Arts Journal – Visual Arts, 18(1), 15-24.
Rafiei Rahmat Talab, Mohammad. (2015). Design of a Residential Complex in Tehran Based on the
 ‌     Concepts of Fractal Geometry in Iranian Architecture. Master’s Thesis, University of Science and
       ‌Art of Yazd.
Zomorshidi, Hossein and Zomorshidi, Zahra. (2012). The Art of Tile Making and Tile Work in Iranian Architecture until the End of the Timurid Period. Journal of Iranian-Islamic City Studies, 3(10), 49-60.
Salingaros, Nikos. (1998). Fractals in New Architecture. Translated by Nasim Chitsazan and Nasim
      ‌Iranmanesh. Memar Bi-Monthly Journal, 26, 27-28.
Saremi, Hamidreza; Hadianpour, Mohammad and Nosrati, Fatemeh. (2014). Application of Fractal
      ‌Geometry in Islamic Architecture. National Conference on Urban Planning, Urban Management
       ‌and Sustainable Development, Tehran, 1-15.
Abeddoust, Hossein and Kazempour, Ziba. (2017). Analysis of the Roots and Concepts of Geometric
      Motifs in Islamic Architecture within Ancient Iranian Art. Negarineh Honar-e Eslami Journal,
       ‌3(10), 41-58.
Farhang, Mahgan and Rezaei, Safieh. (2016). Fractal Art and Software Art with an Approach to
 ‌     Computational Geometry and Pattern Geometry. Exploration in Basic Science Education, 2(4), 11-
      ‌24.
Ghobadian, Vahid. (2013). Fundamentals and Concepts in Contemporary Western Architecture
 ‌     Cultural Research Bureau Publications, Tehran.
Karami Fard, Raham. (2017). The Nature of Fractals and Their Impact on Architecture. Conference on Islamic and Historical Iranian Architectural and Urban Studies, Shiraz.
 
 
Gorouzi, Mehrdad. (2008). Visual Arts: Fractal Art. Ayeneh Khial Journal, 9, 19-30
Mirian, Meysam. (2011). The Role of Fractals in Geometry, Mathematics and Their Relation to
      ‌Islamic Motifs in Iranian Buildings and Mosques. Ketab-e Mah-e Honar Monthly, 159, 86-95.
Noghrekar, Abdolhamid. (2010). Theoretical Foundations of Architecture. Payam Noor University
       ‌Publications, Tehran.
Naghibi Rad, Parastou and Kord Jamshidi, Maria. (2014). Application of Fractal Geometry in the
 ‌     Physical-Spatial Form of Cities. First National Conference on Searching for Tomorrow’s City,
      ‌Tehran, 1-15.
Bovill, Carl. (1996). Fractal geometry in architecture and design, Brikhauser, Boston.
Prusinkiewicz, Przemyslaw. (1987). Applications of L-systems to computer imagery, In H.Ehrig,
 ‌     M.Nagl, A.Rosenfeld, and G .Rozenberg, editors, Graph grammars and their application to computer
       ‌science; Third International Workshop, 534–548, Springer-Verlag, Berlin,
       ‌LectureNotesinComputerScience 291
Prusinkiewicz, Przemyslaw and Lindenmayer, Aristid. (1990). The Algorithmic Beauty of Plants,
 ‌     Springer-Verlag,NewYork.
Bonner, Jay. (2017). Islamic geometric patterns: their historical development and traditional methods of construction. www.pinterest.com (In Persian).