Computing the making of Seljuk geometric patterns

This thesis proposes an integrated computational method for analyzing and generating geometric patterns as material things. The study explores the possible contributions of the computational aspects of formal relations between the shapes and their making to the understanding of the design generation in craft and to the contemporary computational design practice and education. The case study comprises a number of geometric patterns carved into stone on monumental building façades in Anatolia from the Seljuk-period. The limited knowledge on the original making processes of these historical designs provides an important opportunity to use an integrated computational approach for understanding the generative process of the stone carving craft as a cultural heritage. Motivated by the making grammar approach that integrates making in computational design, this thesis investigates its possible applications in analyzing the generative process of making in the particular case of stone carved geometric patterns. The method used in the analysis of the existing patterns relies on analyzing the geometric patterns as material things instead of pure abstract geometries. The study is comprised of three parts. Firstly, a number of existing stone carved patterns from the Seljuk-period have been analyzed by means of the formal relations between their design layout and the making process. The design layouts of the patterns were examined as compass and ruler constructions that are based on generating regular polygons on circular grids. Various shape transformations were presented in the form of shape rules to indicate the possible generative methods of producing the layouts of the patterns. Seven different types of general transformation rules (tessellation, addition, subtraction, translation, extrusion, rotation, curving) have been highlighted. The layouts of the patterns that can be produced by these transformations are considered as the initial shapes of the carving process. Secondly, possible scenarios of material transformations for generating the stone carved patterns from the initial shapes were presented in the form of making rules. Making rules developed for stone carved geometric patterns formalize the material transformations that were generated by various making parameters such as tool shape, tool diameter, cut depth and cut distance. The rule-based computational making method presented in this study introduces tool-based emergence as a new concept for the computational making studies. Finally, the study concludes with examining the application of making rules with today's digital fabrication tools. The application experiments were conducted with a 3-axis CNC milling machine and highlighted the variety of possible pattern generations that were enabled by integrating the knowledge of making parameters such as tool shape, tool diameter, cut depth and other parameters of the milling toolpath generation. The results suggest that the rule-based computational making method presented in this study has several practical applications. Firstly, the integrated computational approach for analyzing the generation process of stone carved Seljuk geometric patterns can be used for developing a comprehensive making grammar of stone carved Seljuk geometric patterns. The method used for this study may be applied to other geometric patterns made with various materials, tools, and techniques in future studies. Formalizing material transformations as making rules has been found useful for reasoning about the formal relations between the surface geometry (curvature, dimension), the rotational symmetry group of the pattern, tools and actions. These findings enhance our understanding of the design generation of stone carved Seljuk geometric patterns. The design generation experiments conducted with the 3-axis CNC milling machine showed that the rule-based computational making method presented in this study can be useful for enhancing computational design processes by means of diversity and integrity. The results of the experiments from two student workshops suggest that the method for generating carved patterns using making rules can be used for establishing an exploratory making approach that can integrate the craft knowledge, the concept of tool-based emergence and CNC milling technology in today's design education. Experiments on integrating shape rules and making rules in design processes during the student workshops have been conducted. Although the study is based on a small sample of participants, the findings suggest that the integration of both rule types enhance design generation by means of diversity. Moreover, both shape transformations and material transformations are interrelated and can continuously feed each other. Lastly, the study suggests a possible contribution to restoration applications by integrating the knowledge of the making of the existing stone-carved patterns. Although the current study is based on a small sample of patterns, the open access database of this research is to be expanded to serve as a base for future collaborations with historians and restorators.