Generating a Functional Grammar for Architectural Design from Structural Hierarchy in Combination of Square and Equal Triangle
Islamic culture was accountable for a plethora of development in astronomy and science in the medieval term, and in geometry likewise. Geometric patterns are reputable in a considerable number of cultures, but in the Islamic culture the patterns have specific features that connect the Islamic faith to mathematics. In Islamic art, three fundamental shapes are generated from the circle shape: triangle, square and hexagon. Originating from their quiddity, each of these geometric shapes has its own specific structure. Even though the geometric patterns were generated from such simple forms as the circle and the square, they can be combined, duplicated, interlaced, and arranged in intricate combinations. So in order to explain geometrical interaction principles between square and equal triangle, in the first definition step, all types of their linear forces individually and in the second step, between them, would be illustrated. In this analysis, some angles will be created from intersection of their directions. All angles are categorized to some groups and the mathematical expressions among them are analyzed. Since the most geometric patterns in Islamic art and architecture are based on the repetition of a single motif, the evaluation results which are obtained from a small portion, is attributable to a large-scale domain while the development of infinitely repeating patterns can represent the unchanging laws. Geometric ornamentation in Islamic art offers the possibility of infinite growth and can accommodate the incorporation of other types of architectural layout as well, so the logic and mathematical relationships which have been obtained from this analysis are applicable in designing some architecture layers and developing the plan design.
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 Ettinghausen, R., Grabar, O., & Jenkins, M. (2001). Islamic art and architecture 650-1250 (Vol. 51). Yale University Press.
 El-Said, I., El-Bouri, T., & Critchlow, K. (1993). Islamic art and architecture: the system of geometric design. Garnet Pub Ltd.
 Broug, E. (2008). Islamic geometric patterns. London: Thames & Hudson. P.2-3
 Johnson, P. A. (1994). The Theory of Architecture: Concepts Themes & Practices. John Wiley & Sons. p. 357
 McMahon, J. A. (2000). Perceptual principles as the basis for genuine judgments of beauty. Journal of Consciousness Studies, 7(8-9), 29-36.
 Mahdavinejad, M., Ahmadzadeh Siyahrood, S., Ghasempourabadi, M., & Poulad, M. (2012). Development of Intelligent Pattern for Modelling a Parametric Program for Public Space (Case study: Isfahan, Mosalla, Iran). In Applied Mechanics and Materials (Vol. 220, pp. 2930-2935). Trans Tech Publications.
 Hillenbrand, R. (1999). Islamic art and architecture. London: Thames and Hudson.
 Kaplan, C. S. (2000). Computer generated Islamic star patterns. Bridges, 105-112.
 Kaplan, C. S., & Salesin, D. H. (2004). Islamic star patterns in absolute geometry. ACM Transactions on Graphics (TOG), 23(2), 97-119.
 Tavasoli, M. (2004). Art of Geometry: (Tehran: Payam, first print, 2004), pp. 5-15.
 Lee, A. J. (1987). Islamic star patterns. Muqarnas, 4, 182-197.
 Critchlow, K. (1976). Islamic patterns. Thames and Hudson.
 Wade, D. (1976). Pattern in Islamic art. Studio Vista.
 Baer, E. (1998). Islamic ornament. Edinburgh University Press.
 Ekhtiar, M. (2011). Masterpieces from the Department of Islamic art in the Metropolitan Museum of Art. Metropolitan Museum of Art. New York.
 Kaplan, C. S. (2005, May). Islamic star patterns from polygons in contact. In Proceedings of graphics interface 2005 (pp. 177-185). Canadian Human-Computer Communications Society.
 Molodi, B. (2002). Application of geometry in Architecture of Iran's past: (Tehran: Building and housing research center, first print, 2002).
 Dabbour, L. M. (2012). Geometric proportions: The underlying structure of design process for Islamic geometric patterns. Frontiers of Architectural Research, 1(4), 380-391.
 Bier, C. (2015). 3 Geometry made manifest. The Historiography of Persian Architecture, 29, 41.
 Cenani, S., & Cagdas, G. (2007, December). A shape grammar study: form generation with geometric Islamic patterns. In Generative Art Conference (Vol. 10). P.2.
 Speller, T. H., Whitney, D., & Crawley, E. (2007). Using shape grammar to derive cellular automata rule patterns. COMPLEX SYSTEMS-CHAMPAIGN-, 17(1/2), 79.
 Stiny, G., & Gips, J. (1972). Shape Grammars and the Generative Specification of Painting and Sculpture,” Information Processing 71, IFIP, North-Holland, Amsterdam. P.127.
 Pupo, R., Pinheiro, E., Mendes, G., Kowaltowski, D. C. C. K., & Celani, G. (2007). A design teaching method using shape grammars. In Proc. 7th Int. Conf. Graphics Engineering for Arts and Design (pp. 1-10). P.3.
 Knight, T. (2000). Shape grammars in education and practice: history and prospects. International Journal of Design Computing, 2(67).
 Cenani, S., & Cagdas, G. (2006). Shape grammar of geometric Islamic ornaments. Proceedings of the 24th eCAADe. P.292, P. 293
 Dullemond, K., & Peeters, K. (1991). Introduction to Tensor calculus. Kees Dullemond and Kasper Peeters. P.42-44.
 Gatt, R., Mizzi, L., Azzopardi, J. I., Azzopardi, K. M., Attard, D., Casha, A., ... & Grima, J. N. (2015). Hierarchical auxetic mechanical metamaterials. Scientific reports, 5, srep08395.
 Lakes, R. (1993). Materials with structural hierarchy. Nature, 361(6412), 511-515.
 Chorbachi, W. A. K. (1989). In the Tower of Babel: Beyond symmetry in Islamic design. Computers & Mathematics with applications, 17(4-6), 751-789.
 Alexander, C., Black, G., & Tsutsui, M. (1995). The Mary Rose Museum (Vol. 8). Oxford University Press, USA.
 Abas, S. J., & Salman, A. (1992, January). Geometric and Group‐theoretic Methods for Computer Graphic Studies of Islamic Symmetric Patterns. In Computer Graphics Forum (Vol. 11, No. 1, pp. 43-53). Blackwell Science Ltd.
 Aljamali, A. M., & Banissi, E. (2004). Grid method classification of Islamic geometric patterns. In Geometric Modeling: Techniques, Applications, Systems and Tools (pp. 233-254). Springer Netherlands.
 Abas, S. J. (2001). Islamic geometrical patterns for the teaching of mathematics of symmetry. Symmetry: Culture and Science, 12(1-2), 53-65.
 Prévost, R., Whiting, E., Lefebvre, S., & Sorkine-Hornung, O. (2013). Make it stand: balancing shapes for 3D fabrication. ACM Transactions on Graphics (TOG), 32(4), 81.
 Akbarzadeh, M., Van Mele, T., & Block, P. (2013). Equilibrium of spatial structures using 3-D reciprocal diagrams. In Proceedings of the international association for shell and spatial structures (IASS) symposium.
 Akbarzadeh, M., Van Mele, T., & Block, P. (2015). On the equilibrium of funicular polyhedral frames and convex polyhedral force diagrams. Computer-Aided Design, 63, 118-128.
 Shin, H. V., Porst, C. F., Vouga, E., Ochsendorf, J., & Durand, F. (2016). Reconciling elastic and equilibrium methods for static analysis. ACM Transactions on Graphics (TOG), 35(2), 13.
 Kappraff, J. (2001). Connections: the geometric bridge between art and science (Vol. 25). World Scientific.
 Ham, D. (2013). Restructuring Beginning Design Curriculums with Visual Calculation. In Intelligent Environments (Workshops) (pp. 588-597).
 Ham, D. A. (2016). How Designers Play: The Ludic Modalities of the Creative Process. Design Issues, 32(4), 16-28.
 Ham, D. (2015). Playful Calculation. In Revolutionizing Arts Education in K-12 Classrooms Through Technological Integration (pp. 125-144). IGI Global.