Fractal Dimension of Islamic Architecture: The case of the Mameluke Madrasas: Al-Sultan Hassan Madrasa

Islamic architecture represents a successful example in extracting the mathematical proportionsand the fractal geometry of the natural organisms. The Mameluke architecture is considered atransitional stage to a more self-similar detailed geometry presented in a diverse scale range. Thatwas the motive behind using the fractal geometry as a patterned grid in Mameluke designs.Therefore, this research objective is to reveal the hidden dimensions within the fractal geometryin Mameluke architecture with special emphasis on Al-sultan Hassan madrasa as a case study.Fractal geometry exists within its geometry in four levels; the internal spaces main subdivisions,floor patterns, al-muqarnas and ornaments. Thus, the research establishes an interactiveparametric model, which has two reversible functions; First, to analyse by tracing the fractalgeometry evolution of Al-sultan Hassan madrasa layout and secondly, to apply the fractaldimension as a design generator to more advanced fractal forms. Al-sultan Hassan madrasarepresents the likelihood of analysing and generating further styles based on its fractal geometry.The process could be applied supplemented with the parameters and limitations change. Hence,an infinite number of design variations are generated based on the fractal geometry of a specificstyle.

PDF

___

K. Trivedi, “Hindu temples: Models of a fractal universe,” The Visual Computer, vol. 5, no. 4, pp. 243-258, (1989).
Crompton, “Fractals and picturesque composition,” Environment and Planning, pp. 451-459, (2002).
W.E. Lorenz, “Fractal Geometry of Architecture,” in Biomimetics – Materials, Structures and Processes, Berlin , Springer-Verlag Berlin Heidelberg , pp. 179-199, (2011).
Sedrez, M. and Pereira, A., “Fractal Shape,” Nexus Network Journal, vol. 14, no. 1, pp. 97-107, (2012).
E. Broug, Islamic Geometric Patterns, Thames & Hudson, (2008).
M. Ben-Hamouche, “Fractal Geometry in Muslim Cities:How Succession Law Shaped Morphology,” Nexus Network Journal, pp. 235-251, (2011).
W. Al-Buzjani, Those Geometric Constructions Which Are Necessary for a Craftsman (manuscript in Arabic), Baghdad: limited published copies, Mid of the 1st century.
L. M. Dabbour, Geometric proportions: The underlying structure of design process for Islamic geometric patterns, vol. 1, Frontiers of Architectural Research, p. 380–391,(2012).
M. Abdelsalam, “The use of smart geometry in Islamic patterns,” Bahrain, (2012).
M. Mirza, “https://destinationksa.com/touring-jeddahs-largest-mosque/#more-35206,” ,(23 JUNE 2017). [Online]. Available: https://destinationksa.com/author/mirza/page/2/.
T. D’Arcy, “On growth and form.,” Cambridge University, (1942).
C. Bovill, Fractal gemetry in Architecture and design, Boston: Birkhauser, (1996).
B. Mandelbrot, The fractal Geometry of Nature, New York : W. H. Freeman, (1982).
Ostwald M.,Vaughan J., The fractal dimension of architecture, Switzerland: Birkhäuser, (2016).
S. H. Nasr, Islamic Cosmological Doctrines, London: Thames Hudson, (1978).
Agha Khan, “CAD drawings,” (2016). [Online].
K. Williams, “Architecture and Mathematics,” Nexus Journal, (2006).
Haider, G. and Moussa M., “Explicit and Implicit Geometric Orders in Mamluk Floors: Secrets of the Sultan Hassan Floor in Cairo,” in Architecture and mathemaics: Volume 1, Birkhauser, , pp. 483- 488,(2015).
Samper A. , Herrer B., “The Fractal Pattern of the French Gothic Cathedrals,” Nexus Network Journal 16, p. 251–271, (2014).
R. Aish, “Bentley’s GenerativeComponents.A design tool for exploratory architecture,” in smart geometry conference, London, (2003).
M. Celani, “Beyond analysis and representation in CAD:a new computational approach to desi2n education,” MIT, Massachusetts, (2002).
M. Colakoglu, “Design by Grammar: Algorithmic Design in an Architectural Context,” MIT, Massachussetes, (2001).
Marques and Woodbury , “Managing contingency in parametric models through implicit relational modeling,” in CAADFutures 07, Canada, (2007).