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１ MINISTRY OF EDUCATION AND TRAINING HANOI UNIVERSITY OF CIVIL ENGINEERING LE THI PHUONG CHI APPLICATION OF FRACTAL GEOMETRY TO ARCHITECTURAL DESIGN COMPOSITION IN VIETNAM Major: Architecture Code: 9580101 SUMMARY OF DOCTORAL DISSERTATION HANOI - 2022 ２ The dissertation was completed at: HANOI UNIVERSITY OF CIVIL ENGINEERING (HUCE) Academic Supervisors: Prof Dr Doan Minh Khoi Assoc Prof Dr Dang Van Cu Peer reviewer 1: Prof Dr Nguyen Quoc Thong Peer reviewer 2: Dr Tran Thanh Binh Peer reviewer 3: Assoc Prof Dr Khuat Tan Hung The doctoral dissertation will be defended before the University Council of Dissertation Assessment at Hanoi University of Civil Engineering at …:…, dd/mm/2022 The dissertation can be found at the Library of Hanoi University of Civil Engineering and the National Library of Vietnam INTRODUCTION Rationale In architecture, geometry is the basic factor for design, “a principle for organizing of spaces and a means of connecting different parts of a building together” In addition to Euclidean geometry, which has been known for thousands of years, non-Euclidean geometry has been established along with the development of science in general, especially computer science, resulting in a large number of unique buildings and new architectural trends across the globe In this development, Fractal geometry can be mentioned as the latest domain of geometry discovered and published for the first time by the mathematician Mandelbrot in the 1970s If other types of geometry, such as Euclidean geometry, study single shapes only, for example, square, circle, etc., then Fractal geometry focuses on more complex objects and shapes, consisting of many or even numerous lines and curves combined on the basis of similarity rules This can be regarded as a stepping stone for the relationship between Fractal geometry and composition in architecture The most crucial point in this geometry is the ability to describe the complex structures of nature, which Euclidean geometry could not Later, Fractal geometry continues to develop vigorously and has been applied to almost all socio-economic sectors, including architecture As terminologically interpreted, “Architecturology” can be understood as the science of architecture Architectural theorist Carl Bovill has stated: “Fractal geometry is perhaps a sole example of a technology that goes straight into the core of design composition, enabling architects or designers to demonstrate a complex understanding of nature", and it can also be used as the basis to widely apply science to artworks Derek Thomas defines architecture that applies Fractal geometry as a “contemporary form of organic design” Fractal geometry was initiated in association with the development of computer graphics and has played an important role in the development history of Parametric Architecture - a movement in architecture closely associated with both design and graphic technology Although the importance and influence of Fractal geometry in the world over the past decades has been undeniable, in Vietnam, especially in architecture, Fractal geometry is quite new There have been no comprehensive or in-depth studies ever undertaken so far Currently, Vietnamese architecture needs to integrate with world architecture and this is becoming urgent If the design is not so frequently updated with new science and technology, it will certainly be a blunder, even a failure when architecture does not keep pace with the global mainstream That is why the PhD student has chosen to investigate this area with a dissertation entitled “Application of Fractal geometry to architectural composition in Vietnam” Goal and objectives 2.1 Goal: To propose possibilities with solutions to apply Fractal geometry to architectural composition in Vietnam, meeting the needs of architectural development in the era of science and technology 4.0 2.2 Objectives: To achieve this goal, the following objectives should be set: - To determine the principles and scope of application of Fractal geometry to building design in Vietnam (level of application, morphological forms, types of composition and buildings) - To find out solutions to apply Fractal geometry to design, with the support of graphic technology, in Vietnam - To propose a mind roadmap for the step-by-step application of Fractal geometry to architectural composition in Vietnam Research objects and scope 3.1 Research object: Architectural composition in which Fractal geometry is applied 3.2 Research scope: Buildings and/or building complexes in Vietnam from now to 2030 with a vision to 2050 Research methods The following methods are used: Data collection, data analysis, classification and systematisation of theories; Site surveys, evaluation and summarisation of development and experience in the history; Comparative study; Modelling and simulation; Expert consultation; Case studies; Forecasting Theoretical and practical significance 5.1 Theoretical significance: Propose a feasible theoretical concept on the application of Fractal geometry to the design process of architectural composition in Vietnam; Consolidate the system of theories and scientific knowledge for teaching; Provide an additional theoretical document which can be used to support the reform of training programmes in architecture 5.2 Practical significance: Explore a new direction to apply Fractal geometry in design, which can be used with graphic design and support the design process of architectural composition for buildings in Vietnam The proposals are highly practical and suitable as a reference and design guide in the era of industrial revolution 4.0 New contributions 6.1 In theory: Systemise the interrelationship between the theory of Fractal geometry and the theory of architectural composition; Propose theoretical solutions and principles of applying Fractal geometry to the study and concept design of architectural composition in Vietnam, helping consolidate scientific knowledge with new elements related to design in the theory of architecture 6.2 In education: Propose the bases and solutions to combine the science of Fractal geometry and the science of architectural design, providing a premise for a new theoretical study subject, supporting the reform of training programmes in architecture until 2030 6.3 In practice: Propose a tool of thinking in design established on the basis of science and technology at each design stage, which is particularly suitable for the revolution 4.0 in Vietnam Structure of the dissertation The core of the dissertation consists of three chapters: - Chapter 1: Overview of the application of Fractal geometry to architectural composition (35 pages); - Chapter 2: Scientific bases for the application of Fractal geometry to architecture composition in Vietnam (51 pages); - Chapter 3: Proposals to apply Fractal geometry in architectural composition (48 pages) Concepts and terms used in the dissertation Composition: An overall structure made up of the combination and organisation of components and elements “Fractal”: is an English word derived from the Latin “fractus” meaning “breaking up” or “disruption” Fractals: An abstract concept in mathematics used to describe things which are composed of many small (and naturally formed) parts and complex when magnified at all scales Each small part is similar to or the same as a larger segment containing it as shown in Figure 0.1 Fig 01 Example of the Fractals in mathematics and nature - Fractal geometry (FG): A branch of mathematics that investigates Fractal geometry objects - Composition in architecture (CA): an aggregation of components that make up the architectural form or shape of a building or a building complex - Design of architectural composition (DAC): an important part of architectural design, as Gaudet defined, it is “the combination of parts in a unified whole” More specifically, DAC is the organisation, layout, and arrangement of the components in the space of a building to achieve unity of both interior and exterior - Development of composition: the process of developing a combination of built forms, including several steps from the simple start to detail as follows: INITIAL CONCEPT SIMPLE SHAPE ORIGINAL COMPOSITION FINAL COMPOSITION - Geometric variation: the transformation of a shape from an object into a new one that is appropriate for a process, a context or a certain form The form can change gradually or suddenly, depending on the idea CHAPTER OVERVIEW OF THE APPLICATION OF FRACTAL GEOMETRY TO ARCHITECTURAL COMPOSITION 1.1 OVERVIEW OF THE ESTABLISHMENT AND DEVELOPMENT OF FRACTAL GEOMETRY 1.1.1 The establishment and development of Fractal geometry The theory of Fractal geometry was built on two major issues in the early 20th century, including the chaos of the regular development processes in nature and the concept expansion of dimensions and measurements in classical Euclidean geometry In fact, the inceptive idea of Fractal geometry in mathematics came in the 17th century By the 1960s, computer graphics were founded and developed Mathematician Mandelbrot, in the course of his studies on the problem of computer image generation, discovered the rules of self-similarity in pre-existing mathematical images as well as structures in nature In 1975, the theory of Fractal geometry was officially established and quickly went beyond the boundary of basic mathematics and penetrated into theory as well as image-based applications in all domains 1.1.2 Comparison of the differences between Fractal geometry, Euclidean geometry and Topo geometry Three areas of geometry are different in the context and time of formation, in the meaning of the name, in the research objects, in the expression, in the ability to design shapes and in the scope of the current application in architecture The strengths of Fractal geometry are reflected in the structure of composition; the variety of shapes and the graphic relevance Despite these differences, all the areas of geometry play really important (and irreplaceable) roles in the human civilisation 1.1.3 Fractal geometry in computer graphics Today there are two major directions in the application of the theory of Fractal geometry in graphic design In particular, image generation on the computer is a vigorous and common application as well as an inspiration for designers in general The bases for building image generation algorithms in Fractal graphics should be considered the principles of Fractal geometry 1.2 CURRENT SITUATION OF APPLYING FRACTAL GEOMETRY TO ARCHITECTURAL COMPOSITION WORLDWIDE AND IN VIETNAM 1.2.1 Current situation of applying Fractal geometry to architectural composition worldwide Before 1975 (when the theory of Fractal geometry was established): Many old buildings and even modern buildings before 1975 seemed to be designed on self-similarity However, just like in mathematics, without graphic design as a tool, people in the past were not able to generalise the dialectical relationship between structures in nature and laws in geometry Fractal geometry only manifested in individual creative (but somehow spontaneous) designs or passive imitations learning from a certain architectural style which did not make use of the wide range of transformations that Fractal geometry can offer for application After 1975: Researchers and designers have applied the rules of Fractal shaping more intentionally and carefully to fulfil the requirements in simulating complex structures in nature from a scientific perspective with the aid of computers to generate extraordinary graphical designs which are both nature-based and technology-based Since 2000, Fractal architecture with its enormous influence in terms of self-similarity-based design continues to grow, as seen in organic architecture, ecological architecture and parametric architecture at different levels, from simple to complex structures Fig 1.1 Illustrations of modern architecture with an application of Fractal geometry at a simple level and a higher level 1.2.2 Current situation of applying Fractal geometry to architectural composition in Vietnam Fractal geometry has not been widely known in Vietnam However, in practice, buildings with Fractal characteristics to a certain extent (especially those showing self-similarity) can be seen in both ancient and modern Vietnamese architecture Most of these features not come from a deep understanding of Fractal geometry but actually from traditional Asian design philosophies 1.2.2.1 Signs of Fractal geometry in Vietnamese ancient architecture Self-similarity elements on various scales can be found in many ancient buildings, such as temples and towers, as well as French colonial buildings in Vietnam 1.2.2.2 Signs of Fractal geometry in Vietnamese modern 12 b According to the rules of similarity c By origin 2.1.2 Theoretical bases of architectural composition 2.1.2.1 Language and rules of architectural composition - Language: Point; Line; Face/Surface; 3D Shape - Rules of shaping: Layout (Radiant; Linear; Radial; Cluster; Grid) Principles of organisation (Axis; Symmetry; Hierarchy; Rhythm) 2.1.2.2 Characteristics of architectural composition a Architectural composition and function: There are many patterns of composition They can be distinguished by layout and principles of organisation, and appropriate for building design with specific functions and various forms, such as centralised layout, the chain of interconnected rooms, corridor-based layout and single unit layout b Architectural composition and form: The geometrical lines and curves within a composition all play certain roles and have some effects in terms of aesthetics, and prove to be consistent with the function(s) of the building The aesthetics of forms in architectural composition include unity and variation; harmony and symmetry; stability and balance 2.1.2.3 Development of architectural composition The development of composition can be divided into several stages: concept design, preliminary design and detailed design Developing a composition may use the following methods: grid diagrams and similar shapes, repetition of typical elements while individual elements are regarded as highlights 2.1.2.4 Variations of architectural composition 13 Linear, facial and solid 3D shape variations can be created by using geometric transformation, such as creating mesh dislocation, shape rotation, axis rotation, or even transformation of basic shapes into freeform shapes with various curves 2.1.3 Comparison between Fractal composition and architectural composition 2.1.3.1 Compatibility The compatibility is an argument for considering the possibility of applying Fractal composition to architectural design The compatibility can be reflected through the similarity of the two types of composition in a number of aspects Many Fractal composition cases, especially those in mathematics, can satisfy most of the aesthetic principles of composition in architectural theory (language, layout, link principles, organisation, development of composition and variation) 2.1.3.2 Difference This is an argument which needs to be consolidated and take note of while applying Fractal geometry to design of composition Fractal compositions themselves are still purely geometrical structures, not yet able to meet the requirements of an architectural composition, thus they need designers to ensure the requirements in use or operation The difference between Fractal composition and architectural composition is demonstrated in the different shapes, scales and functions, as well as aesthetics 2.2 PRACTICAL EXPERIENCE 2.2.1 Classification criteria and bases for practising Fractal geometry 14 From the analysis of practice in such aspects as functions, types of building; forms of composition; design concepts; etc., it is possible to take the following notes: a Basis for application: The compatibility in shape (morphology, structure, function), aesthetics, mental significance, styles and symbols to be carried to the public b Criteria for classifying experience in applying Fractal geometry to composition design from practice: Level of application of Fractal geometry; Characteristics of the scale of architectural composition; Characteristics of styles in applied architectural composition 2.2.2 Experience in composition design based on the level of flexibility in the application of Fractal geometry 2.2.2.1 Prototype application Designers take the prototype of the typical Fractal composition available for the design of architectural composition Lessons learnt from practice: Applying the same basic form of Fractal composition to the design, in order to create unique features and adapt to the context, designers can choose various solutions for the application, such as changing a position, a dimension, a size, a material, a colour, etc., to enrich or diversify architectural composition 2.2.2.2 Creative application Designers have to create a Fractal composition (initiator, generator, and level) to convey their own ideas associated with a particular building The lesson learnt from practice: This process seems like part of a parametric design approach If one of the components has changed, 15 a new combination can be created Therefore, it is possible to apply graphics to research and to make an appropriate option 2.2.2.3 Flexible and free application Designers mainly use self-similarity as one property in Fractal geometry Lessons learnt from practice: Flexible and free application of Fractal geometry shows randomness as one property without following any certain rules Graphics can help create and determine appropriate shapes with a high level of flexibility 2.2.3 Experience in architectural composition design based on the flexible development of architectural forms 2.2.3.1 Architecture developing in width and length - Practical experience: using similar modules on different scale These modules can be put together in a grid layout or stacked layer structure, resulting in various compositions of any size 2.2.3.2 Architecture developing in height - Practical experience: Applying Fractal geometry in high-rise building design for horizontal and vertical division / forming a grid of similar shapes for the building envelope / creating a terrace built form in stacked layer structure / creating hollow module-based structures for towers 2.2.3.3 Architecture developing in large-scale blocks - Practical experience: The application of Fractal similar-shape grid diagrams to the building envelope is both compatible in structural design and creative in faỗade design with different divisions and rhythms, showing high-tech features and looking more attractive than monotone faỗade design 2.2.4 Experience in composition design based on the flexible development of architectural styles 2.2.4.1 Organic/biomimetic architecture - Practical experience: 16 - An appropriate design concept could be developed on the basis of similarity in shape and structure between the composition learnt from nature and Fractal composition - An appropriate location for application could be selected on the basis of compatibility of the structure, shape and function of each part or component to be applied 2.2.4.2 Architecture based on traditional shaping - Practical experience: The self-similarity on various scales is widely applied to make religious buildings and palaces more majestic and magnificent The use of self-similarity also varies from place to place, creating a kind of distinct identity, both geographically and religiously 2.2.4.3 Technology-based architecture - Practical experience: Technology-based architecture is often associated with parametric design methods as well as the computer-based graphic programs In addition, the patterns of connection, either in mesh or in branch structure, that are unique and similar to nature can be seen in Fractal compositions and compared with frame structures, which can be employed to design buildings in deconstruction style 2.3 FACTORS WITH EFFECTS ON THE APPLICATION OF FRACTAL GEOMETRY TO ARCHITECTURAL COMPOSITION DESIGN IN VIETNAM 2.3.1 Natural condition The diversity of natural conditions (topography, climate, rivers, soils, organisms, etc.) and the differences between regions are outstanding natural features in Vietnam, which must be carefully considered in architectural design in general, and the level of application of Fractal geometry to building design in particular 2.3.2 Socio-cultural and human factors 17 The typical characteristics of Vietnamese culture (wet-rice civilisation, open culture, unity in diversity, etc.) differ from region to region, and minor ethnic groups have their own cultures which will have an influence on the local architectural styles and built forms Human factors (investors, approvers, designers) play a direct and decisive role in architectural design and the level of application of Fractal geometry (if any) 2.3.3 Development of technology The application of Fractal geometry in Vietnam also needs to be closely associated with the context of domestic technology Some aspects to consider: Development of design and graphic technology and development of construction technology in Vietnam 2.4 LEGAL BASES AND DEMAND FOR APPLICATION OF FRACTAL GEOMETRY TO ARCHITECTURAL COMPOSITION IN VIETNAM In consideration of the development orientation for Vietnamese architecture towards modernity and identity, the application of Fractal geometry to architecture should be the application of new scientific knowledge to achieve the goals and comply with the points of view as set in the orientation strategy With a vision towards 2050, it is possible to realise that the demand for the development of science and technology, especially digital technology in architecture, including training is extremely necessary Studying Fractal geometry provides a scientific and theoretical background in design with the support of graphics for the reform of education programmes in architecture in order to meet the requirements of the 4.0 era 2.5 OVERVIEW OF KEY ISSUES IN RESEARCH BASES 18 Theoretical research provides a strong foundation for the application of Fractal geometry to the architectural composition process Studies on practice and factors that influence the process should be undertaken to learn important lessons for the application, and this can be a solid argument to propose viewpoints, principles, possibilities, scope and methods of applying Fractal geometry to architectural composition in the built environment in Vietnam CHAPTER APPLICATION OF FRACTAL GEOMETRY TO ARCHITECTURAL COMPOSITION 3.1 VIEWPOINTS AND PRINCIPLES FOR APPLICATION 3.1.1 Viewpoints - Fractal geometry application should only be regarded as a tool supporting design; - Fractal geometry application is not the only approach and should be flexibly applied; - Fractal geometry application should be made as appropriate for Vietnamese contexts and conditions as possible 3.1.2 Principles - The application has to be in accordance with natural conditions and local cultural characteristics which can be quite different between regions in Vietnam; - The application has to ensure sustainability; - The application has to be suitable at each stage of design (Three phases: concept design, preliminary design and detailed design); - The application has to be diverse in levels; - The application has to be flexible in interaction in use and apply technology ... FRACTAL GEOMETRY TO ARCHITECTURAL COMPOSITION 1.1 OVERVIEW OF THE ESTABLISHMENT AND DEVELOPMENT OF FRACTAL GEOMETRY 1.1.1 The establishment and development of Fractal geometry The theory of Fractal. .. as shown in Figure 0.1 Fig 01 Example of the Fractals in mathematics and nature - Fractal geometry (FG): A branch of mathematics that investigates Fractal geometry objects - Composition in architecture... for building image generation algorithms in Fractal graphics should be considered the principles of Fractal geometry 1.2 CURRENT SITUATION OF APPLYING FRACTAL GEOMETRY TO ARCHITECTURAL COMPOSITION