## Fractal analysis of stone decoration samples of the Seljuk period: the case of Sivas Gökmedrese

Institution Of The Thesis: Gazi University, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2022

Thesis Language: Turkish

Student: Merve ARSLAN

Supervisor: Arzu Özen Yavuz

Abstract:

Architecture has shown a constant change and development since the past; different design criteria have been dominant in each period. Although the design methods vary, the designer has always benefited from mathematics and geometry in his works. It is seen that simple Euclidean geometry was used effectively from the form to the smallest detail of many buildings in the past. On the other hand, when the design fictions in the periods when the Euclid effect in architecture were reduced, it is seen that many designers took the geometry of nature as an example. The geometry of nature is much more complex than the circle, square and many other simple geometric shapes. Fractals can be found in nature, architecture, etc., which Euclidean geometry cannot describe. It has the ability to identify irregular shapes that appear in many places. Fractal geometry, seemingly irregular; but by applying certain rules through repetition and self-similarity, it enables to explain the complex constructs that constitute the order in themselves. With this feature, fractals are a frequently used method to understand and analyze architecture. When fractals are evaluated from different perspectives in architecture; It can be used for the analysis of mass ratios, plan, section and structural ratios, proportions in façade elements or in details (ornamentation) formed in historical processes at settlement scale, building scale. In the thesis study, it is aimed to analyze the geometrical stone decorations of the Anatolian Seljuk Period with the fractal method. The reason for choosing fractal geometry as a method is that there is a geometrical order created with simple rules such as repetition in the structure of decorations that seem to be very complex. In the study, samples from the stone decorations of Sivas Gökmedrese, a product of the Anatolian Seljuk Period, were selected and analyzed. Sivas Gökmedrese, which is the subject of the field study, is a special structure that has great importance among the works of the Anatolian Seljuk Period, and has a lot of geometric decorations with fine stonework and needs to be protected. Within the scope of the study, twodimensional geometric stone decorations on the portal, especially on the front facade of Sivas Gökmederese, were analyzed. When the analyzed ornaments are examined, it is seen that the four main rules of fractal are found in the formation of the ornaments: fractal fraction, self-similarity, repetition (iteration), number of cycles. Thanks to this study, it is thought that two-dimensional and three-dimensional decorations of another Islamic structure built in the same or different period can be analyzed by using fractal geometry from a different perspective.

 Key Words : Architectural analysis, computer aided design, fractal, self-similarity, Anatolian Seljuk period, geometric composition, ornamentation