Function of Fractals: Application of Non-linear Geometry in Continental Architecture
Authors: Mohammadsadegh Zanganehfar
Since the introduction of fractal geometry in 1970, numerous efforts have been made by architects and researchers to transfer this area of mathematical knowledge in the discipline of architecture and postmodernist discourse. The discourse of complexity and architecture is one of the most significant ongoing discourses in the discipline of architecture from the 70's until today and has generated significant styles such as deconstructivism and parametricism in architecture. During these years, several projects were designed and presented by designers and architects using fractal geometry, but due to the lack of sufficient knowledge and appropriate comprehension of the features and characteristics of this nonlinear geometry, none of the fractal-based designs have been successful and satisfying. Fractal geometry as a geometric technology has a long presence in the history of architecture. The current research attempts to identify and discover the characteristics, features, potentials and functionality of fractals despite their aesthetic aspect by examining case studies of pre-modern architecture in Asia and investigating the function of fractals.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 405
 S. S. Mirmoradi, “Recognition of the role of nature in the formation of fractal architecture,” Organ. Technol. Manag. Constr. an Int. J., vol. 9, no. 1, pp. 1574–1583, 2017, doi: 10.1515/otmcj-2016-0020.
 J. Michael, “‘Fractal Architecture’: Late Twentieth Century Connections Between Architecture and Fractal Geometry,” NEXUS Netw. J., vol. 3, no. 1, pp. 73–83, 2001.
 N. Sala, “Fractal Geometry and Self-Similarity in Architecture: An Overview across the Centuries,” Int. Soc. Arts, Math. Ardlitecture, pp. 235–244, 2003.
 A. Osama, L. Sherif, and S. Ezzeldin, “Fractal geometry in architecture: from formative idea to superficial skin design,” ARCHDESIGN, vol. 14, no. 1, pp. 39–49, 2004.
 X. Lu, D. Clements-Croome, and M. Viljanen, “Fractal geometry and architecture design: Case study review,” 4th Chaotic Model. Simul. Int. Conf., no. June 2011, pp. 255–268, 2012.
 A. Belma, “Fractals and Fractal Design in Architecture,” 13th Int. Conf. “Standardization, Protypes Qual. A Means Balk. Countries’ Collab., pp. 282–291, 2016.
 M. Yu and K. J. Aldeen, “A Method of Compositional Fractal Analysis and its Application in Islamic Architectural Ensembles,” IEJME — Math. Educ., vol. 11, no. 5, pp. 1087–1099, 2016.
 B. B. Mandelbrot, The Fractal Geometry of Nature. Times Books, 1982.
 B. B. Mandelbrot, Fractals: Form, Chance and Dimension. W.H.Freeman, 1975.
 B. B. Mandelbrot, “Fractal geometry: what is it, and what does it do?,” Londin, 1989.
 Z. Kiani and P. Amiriparyan, “The Structural and Spatial Analysing of Fractal Geometry in Organizing of Iranian Traditional Architecture,” Procedia - Soc. Behav. Sci., vol. 216, no. October 2015, pp. 766–777, 2016, doi: 10.1016/j.sbspro.2015.12.074.
 D. S. Heinz-Otto Peitgen, Hartmut Jürgens, Chaos and Fractals: New Frontiers of Science. Springer, 2012.
 P. Nagy and P. Tasnádi, “The world of fractals,” in 6th International Conference on Higher Education Advances, 2020, pp. 939–947, doi: http://dx.doi.org/10.4995/HEAd20.2020.11178.
 Garnett P. Williams, Chaos Theory Tamed. Washington, D.C.: Joseph Henry Press, 1997.
 W. E. Lorenz, J. Andres, and G. Franck, “Fractal Aesthetics in Architecture,” Appl. Math. Inf. Sci., vol. 11, no. 4, pp. 971–981, 2017.
 D. S. Lai, A. K. H. Leung, D. Chan, and S. H. Ching, “Cultural Heritage Preservation Using New Media Methods: Yingxian Wooden Pagoda, China,” Virtual Archaeol. Rev., vol. 10, no. 21, pp. 103–115, 2019.
 J. Yuan, Y. Fang, Y. Shi, W. Chen, and J. Wang, “Finite element analysis model of Ying-Xing timber pagoda based on the conformation character and damaged condition,” Ing. Sismica, vol. 30, no. 4, pp. 99–108, 2013.
 X. Mi, X. Meng, Q. Yang, T. Li, and J. Wang, “Analysis of the Residual Deformation of Yingxian Wood Pagoda,” Adv. Civ. Eng., vol. 2020, 2020, doi: 10.1155/2020/2341375.
 P. Id et al., “Educational Application of Virtual Reality in Graphical Simulation of the Construction Process of Chinese Dougong Educational Application of Virtual Reality in Graphical Simulation of the Construction I. Introduction,” Am. Soc. Eng. Educ., 2017.
 A. Roberts, “www.flickr.com,” 2011. https://www.flickr.com/photos/pondspider/6807676466.
 W. Xie, W. S. Chang, and T. H. Wang, “Static behaviour of a two-tiered Dougong system reinforced by super-elastic alloy,” Proc. Inst. Civ. Eng. - Eng. Hist. Herit., vol. 172, no. 4, pp. 164–173, 2019, doi: 10.1680/jenhh.19.00006.
 P. Bjelica, “How ancient Chinese craftsmen developed the technique of earthquake-resistant architecture,” 2017. https://www.wallswithstories.com/ancient/how-ancient-chinese-craftsmen-developed-the-technique-of-earthquake-resistant-architecture.html.
 I. Rian and M. Sassone, “Tree-inspired dendriforms and fractal-like branching structures in architecture: A brief historical overview,” Front. Archit. Res., vol. 3, no. 3, pp. 298–323, 2014, doi: 10.1016/j.foar.2014.03.006.
 Y. Zhang, H. Tang, S. Xue, and Y. Xun, “Investigation into the architectural design of a traditional Japanese wooden pagoda,” J. Asian Archit. Build. Eng., vol. 14, no. 2, pp. 241–246, 2015, doi: 10.3130/jaabe.14.241.
 J. Zhao, D. Lombardi, and A. Agkathidis, “Application of Robotic Technologies for the Fabrication Of,” Cult. / Shift through Ubiquitous Comput. Scripting Ling. Fr., vol. 2, pp. 351–360, 2011.
 Z. Yao et al., “Status investigation and damage analysis of the dougong under the external eaves of the main hall of Chuzu Temple in the Shaolin Temple complex,” BioResources, vol. 14, no. 2, pp. 4110–4123, 2019, doi: 10.15376/biores.14.2.4110-4123.
 J. L. Martin, S. C. McCutcheon, and R. W. Schottman, “Measurement and Analysis of Ancient Chinese Timber-Frame Building,” in A Pictorial History of Chinese Architecture, Beijing: Joint Publishing Company, 2018, pp. 93–150.
 A. S. The, B. Of, and R. Activities, “Rational and Aesthetic Principles of Form-Making in Traditional Chinese Architecture as the Basis of Restoration Activities,” Int. J. Conserv. Sci., vol. 11, no. 2, pp. 499–512, 2020.
 N. C. Garden, “ow to study the problem of fighting arches in ‘Building French Style,’” zhuanlan.zhihu.com, 2015. https://zhuanlan.zhihu.com/p/347804686.
 A. Shahhamze, “Our Iran, Borujerdi house,” 2019. https://www.yjc.news/fa/news/6910856.
 M. R. Bemanian, T. Modares, B. Branch, and B. Branch, “Compatible Ecological Strategies Used in the Design of Traditional Houses in Iran’s Hot and Dry Climate Case Study: The Boroujerdis House in Kashan,” J. Archit. Constr., vol. 1, no. 1, pp. 43–55, 2018.
 M. R. Ardebili and M. Shafiei, “Lessons from the Past: Climatic Response of Iranian Vernacular Houses to Hot Climate Conditions,” Sp. Ontol. Int. J., vol. 5, no. 4, pp. 15–28, 2016.
 F. Sakhai, “Descriptive Survey on Hostorical Borujerdi’s House,” Arthur Construction Brand, 2014. https://iranmemari.com/khane-burujerdiha/.
 M. Raisi, M. R. Bemanian, and F. Tehrani, “A review of the concept of karbandi based on theoretical, practical geometry and structural,” Iran. J. Restor. Archit., vol. 5, no. 1, p. 23, 2013.
 A. Amjad Mohammadi, A. Ebrahiminejad, and Y. Shahbazi, “Karbandi geometry in Iranian architecture; Answering the challenge of formal and stellar application,” Sci. Quarterly, Sci. hub Islam. Archit., vol. 26, no. 1, 2020.
 A. Amjad Mohammadi, A. Ebrahiminejad, and Y. Shahbazi, “Application of karbandi in Iranian architecture; Deployment in the role of shaping,” in 5th.International Congress on Civil Engineering, Architecture and Urban Development, 2017, p. 7.
 N. Hashemi, “Borujedi’s House of Kashan, Symbol of Love in Qajar Era,” 2021. https://www.alibaba.ir/mag/borijerdiha-house-in-kashan/.
 S. Mohammadian Mansour and S. Faramarzi, “Typology and compilation of karbandi geometric structure in Iranian architecture,” J. Fine arts, vol. 48, no. 1, p. 8, 2012.
 A. Salavati, “Investigation of methods and details of karbandi coatings with emphasis on the beam of bearing arches in contemporary and historical examples,” Athar J., vol. 62, no. 1, pp. 53–68, 2014.
 S. Faramarzi and F. Tehrani, “Geometric and structural features of karbandi in Qajar period,” Golestan Art, vol. 17, no. 1, 2019.
 A. Azadifar, A. Omranipor, M. Masoudinezhad, and M. Vafamehr, “Recognition of the effect of skylights on the architecture of Kashan historic houses (Case study: Boroujerdi house),” Haft Hesar J. Environ. Stud., vol. 9, no. 33, pp. 109–124, 2020, doi: 10.29252/hafthesar.9.33.109.
 M. R. Moshkforoush and Z. Javani, “The status of the Aiwan of Aliquapo Palace, Isfahan, in Relation with the Palace Construction and the Surrounding Area from a Structural and Operational Perspective,” in IX International Forum Le Vie dei Mercanti Aversa, 2011, no. June.
 Elmira, “Ali Qapu Palace; a Picturesque Exposure,” 2019. https://irantourismer.com/ali-qapu-palace/.
 Karnaval.ir, “Everyhting About Ali Qapu Palace of Isfahan,” 2018. https://www.karnaval.ir/things-to-do/ali-ghapu-isfahan.
 S. Alaçam and O. Z. Güzelci, “Generative Manifolds of Muqarnas Patterns,” Medios Digit. Arte, Identidad Cult. Umberto Luigi Roncoroni Osio (Ed.), Fondo Editor. USMP, pp. 33–46, 2018, (Online). Available: https://www.academia.edu/39967826/Generative_Manifolds_of_Muqarnas_Patterns.
 O. Z. Güzelci and S. Alaçam, “A Study on Measuring Complexity in Muqarnas Patterns,” Turkish Online J. Des. Art Commun., vol. 9, no. 2, pp. 191–201, 2019, doi: 10.7456/10902100/011.
 Memarsabz.com, “Ali Qapu Analysis,” 2021. https://memarsabz.com/aliqapou/.
 A. Gámiz-Gordo, I. Ferrer-Pérez-Blanco, and J. F. Reinoso-Gordo, “The pavilions at the alhambra’s court of the lions: Graphic analysis of muqarnas,” Sustain., vol. 12, no. 16, 2020, doi: 10.3390/su12166556.
 B. M. Sakkal, Geometry of Muqarnas in Islamic Architecture. 1982.
 M. Modiri ganji, “5 Incredibly Beautiful Destinations in Iran,” 2016. https://www.tasnimnews.com/en/news/2016/10/25/1221339/5-incredibly-beautiful-destinations-in-iran.
 E. Zamanigoldeh and T. Dounas, “Parametric Iranian-Islamic Muqarnas as Drivers for Design for Fabrication and Assembly via UAVS Parametric Analysis and Synthesis of Iranian-Islamic Muqarnas Parametric Analysis and Synthesis of Iranian-Islamic,” 2021, no. March.
 S. Abedi and S. Jamei, “Investigating the acoustic effect in Aali Qapu mansion in Isfahan,” in 1st International Conference on Human, Architecture, Civil Engineering and City, 2015, p. 8.
 H. Azad, “Ali Qapu: Persian Historical Music Room,” akutek, 2008. www.akutek.info.
 S. Rahmat abadi, B. Chalish, and T. Rahmat abadi, “Similar paradigms in structure and architectural arrays; Aali Qapu and Sheikh safi house case study,” 2013, (Online). Available: https://civilica.com/doc/214280