| Quasiperiodic Tilings | Byera Hadley Travelling Scholarship Report | Synopsis |
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There are a diverse variety of pentagonal and decagonal tiling patterns in medieval Islamic architecture. The remarkably similar properties of Timurid-period tilings and contemporary Penrose tilings suggests that quasiperiodic tilings were known to Persian mathematicians and architects five hundred years prior to their western counterparts. Quasiperiodic tilings display infinite variation and self-similarity, where similar patterns recur over multiple scales.The first part of this report focuses on several tilings from the Friday Mosque in Esfahan, Iran, and confirms their compatibility with a recently posited theory that complex tilings with five-fold symmetry were constructed using various permutations of five template ‘girih’ tiles. The girih tile method alleviates the difficulties associated with traditional techniques of tile patterning using a ruler and compass, where slight errors in angle would propagate and be magnified over the thousands of lines that comprise the most elaborate tilings. The girih tile theory also naturally accounts for those tilings that exhibit two spatial tiling scales, where each large-scale girih tile can be neatly divided into a quasiperiodic arrangement of small-scale girih tiles.
These techniques resonate with contemporary architectural thought regarding algorithmic form generation methods and parametric systems. The parametric nature of the Timurid-period tilings is evident in the dual relationship between decoration and structure, where nodal points of the large-scale girih tiles constrain the arch geometry in a similar manner to the control points of spline curves. Previously studied girih tilings exhibit either a periodic or quasiperiodic arrangement of girih tiles at the larger tiling scale. In contrast, two tilings analysed in this report display a less rigid adherence to the mathematical geometry, and reveal the role of a designer’s discretion. One of these tilings, which appears to be a free-form arrangement of girih tiles, strengthens the girih tile theory because its simplicity makes alternative generation methods appear elaborately contrived. In the second example, the quasiperiodic symmetry is broken with the insertion of an irregular girih tile to optimise the compatibility between the building structure and decoration. Again, this interplay mirrors contemporary ideas on massaging the often messy synthesis between algorithmic and parametric form generation and real-world architecture. The second part of this report explores the generative potential of quasiperiodic tilings in two and three dimensions in a contemporary architectural context, utilizing current mathematical knowledge of quasiperiodic tilings and digital techniques. Graphically intuitive algorithmic methods for generating Penrose tilings of arbitrary extent and their self-similar deflations are outlined, together with a technique to generate quasiperiodic girih tilings of arbitrary extent. |
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Special Project | Master of Architecture | University of Technology Sydney | Spring 2008 | Instructor: Anthony Burke
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