EVALUATION OF EFFICIENCY FACTOR IN TILE PATTERN DESIGN USING SYMMETRY GROUP THEORY AND ALGORITHM-ASSISTED DESIGN TOOLS

Abstract

Formation methods of nature are boundless. In this abundance, symmetry, directly associated with cost and time efficiency, lies behind all activities in physical environments. Throughout history, symmetry is considered a factor of harmony and order in human-made environments as a visual, spiritual, and functional tool, has been seen as a connecting path between the designer and nature. Biomimetic processes involving symmetry, have been shaped by aesthetic and structural expectations, providing compactness and productive contributions to the design processes besides its visual and semantic benefits. Today, some productive design tools used in design processes offer the opportunity to rethink the aims of symmetry in nature to provide the highest efficiency with the least energy for human-made environments. The study aims to investigate the possible methodological contributions of symmetry to the cycle between nature and design. It overlaps the material, energy and time-saving factors of natural modularity with the architectural surface design process. In this study, qualitative and quantitative findings about the concept of symmetry at the intersection of various fields such as natural sciences, art, and mathematics, as well as various worldviews examining the aesthetic and pragmatic nature of the concept, were used. The study is based on productive design problems such as to achieve more results with fewer steps in tesselation design and to cover more space by using molding and using fewer prototypes. Algorithm-aided design software called McNeel Grasshopper and up-to-date notations of symmetry group theory were used to solve these problems. In the generative design method, the curve attraction method, in which the curves are effective in formation, is projected to the Z coordinate with sinus and bezier graphics, and three-dimensional surface modules that can be combined with each other are created. In this way, a total of 360 printable digital tiling patterns were produced and classified according to the symmetry group theory. Experimental prototypes were produced for some models. For the algorithm-based design process developed, an experimental method that investigates the production ways in digital and physical environments for module and surface design has been designed. The main purpose of this method is to ensure that strings in different crystallographic manners can be reproduced repetitively with square and rectangular bases. In order to adapt this theoretical model related to nature to the design process, generative design devices that allow controllable hereditary relations through numerical values are used in the production of form. The generative design method allowed analogical simplifications of symmetry and modularity in nature, enabling symmetrical activities to be evaluated through inherited similarities to those in nature. With the algorithm designed on the pragmatic basis of the physical limits of nature, a systematic template that can be used in different spatial systems has been produced. It has been concluded that natural and artificial surfaces can play similar roles within the framework of time and cost efficiency, but numerical values should be observed in structures with different symmetry types in order to facilitate production.