Computational design: Math as a design tool

"When God calculates and exercises his thought, the world is created" Gottfiried Leibniz (Rocker, 2006, s.18 as in case). "Today, when architects calculate and exercise their thoughts, everything turns into algorithms!" (Rocker, 2006, s.18). The main purpose and the interest of humanity is understanding and analysing the universe. While studying the laws of the universe, entire disciplines are guiding people that produce by learning from the nature. The guidance of the form which is expression of architectural design, is made by geometry, mathematics and physics. For this reason, geometry in search of form, has been the fundamental research field of architecture from the ancient age. Phaedrus says that geometry is the creation of human mind, to perceive the world (Corbusier, 1948). With this approach, the statement of the "language of form"should not be a mistake. While the relations of geometry and mathematics is considered, it could be said that "mathematics is the language of geometry". With this way, the relationship between mathematics and architecture that describes its language through form, is formed. At the present time, mathematics becomes a "design tool" not a design language, with the computational design idea. The reason of that, the technological evoluation and digital revolution. With digital design tools, we started to communicate directly with datas and this communication can be only with algorithmic thinking. Algorithmic thinking is based on mathematical thinking, so all new terminologies and relations are connecting architecture and mathematics. As a result, not just in architectural field, in all areas, humanity starts to handle the technology with the power of accuracy of mathematics. In architecture, mathematical systems are started to create to solve design problems. In other words, design approaches turn out from abstract ideas to controllable datas. With the helping of working with datas, design process started to be designed. Information types are changed and new types are occured. Thus, flexibility that is provided by form system derived from mathematical language, enables designing a process that contains the information of producing form. So, as well as the significance of final product itself, with computational design, also process design starts to be discussed. The process of the emergence of product, the design of process, the information of the producibility of final product become new fields in the practice of architecture. For this reason, as architects we are facing with these new fields. In other words, design starts to be designed. These new fields are composed by the evolution of the role of mathematics in design process. In addition to that, a new system of thinking and a new language start to be occured in design process which is dominated by mathematics. The influence of the absoluteity of mathematics to these system of thinking and system of language ensure that the design is subject to the rules. The creation of the design process with set of rules array is addressing of algorithmic thinking (Jabi, 2013, s.22). Algorithmic thinking can be defined as decoding information which creates form with set of rules. In digital age, the possibility of generating form with algorithms, changes the design process. Form is no longer being "made", but "found", based on set of rules or algorithms (Agkathidis, 2015, s.17). In this context, news and reneweds, in other words, the potentials of the algorithmic thinking in the design process, have become a field that must be discovered. When it is desired to enter into the spirit of computational design, it is necessary to create a connection with mathematics, because inevitable communication process begins with mathematics. For this reason, the communication established between the form and the designer through mathematical language has been under consideration. Generating form with mathematical language is the starting point of this thesis. Mathematics that is the language of geometry is tried to be discovered as a language of design. Searched form by mathematical language, designed form is tried to be understand with mathematics. How the steps that generate form can be manipulated during design process is tried to be discovered. How form can be controled with mathematics that is seen as computational design tool? What is opportunities and constraints of form generation with method of computational design? Responses of such these questions have been searched under computatioal design field. As a result, the essence purpose of this thesis is searching influences of design language which is changing by computational design on form generation. Design by mathematics which is a formal language is changing directly to the design process and design idea. In the content of thesis, as a first step, the thinking system which is generated by new design action was examed. Then the language of this new system of thought has been the topic of discussion. All of these researches were originally made from the window of many different disciplines, not only in architectural area, because of the fact that computational design is seen as a system of thought in itself. That's why as a system of thought, computational thinking is subject of all disciplines, creates new practises in all disciplines and become a major field to search and study by experts. Computational design is just the response of computational thinking in the field of architecture. After deep understanding of thinking system and the comminication way of this thinkig, reflections of controversial issues in the real world of computational thinking are handled within the frame of architectural space. Within the context of the thesis, a shell design proposal and a transactional design process sampling were done with computational design techniques. A form generator system was designed during the shell design process. The system is set uped with algorithms to generate form rather than creating one ideal form. The approach of "form is searched" is embodied. Because rather than modeling a just one form, to reach the optimized form, an algorithmic system was created using Rhino Grasshopper plug-in. This system is founded by the computational thinking and formal languge which are seen as the bases of computational design. With this manner, the algorithm which is used for the shell design can be seen as a system to show ruled geometry generation by mathematics, the information of the feasibility of design and process design which are discussed in the thesis in an effective way. As a result, humanity is in a new age and living in a data driven spaces. New age created new fields and new business models. The disciplines that is the part of the new world can be survived. With this manner, what is the way of adaptation to the new system should be the path which all disciplines should follow. In architecture, computational design offers the way to connect architects to this path. For this reason, in fact computational design is a platform in today's architecture, not just an expert field. To communicate with this platform, the thinking behind the approach must be scrutinised. In that time, mathematics shows itself as a foundation of computational thinking and computational designers face with mathematical thought and language. This thesis is placing itself as a guide to first deep meeting with computational design.