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Trang 1MINISTRY 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
Trang 2The dissertation was completed at:
HANOI UNIVERSITY OF CIVIL ENGINEERING (HUCE)
Academic Supervisors:
1 Prof Dr Doan Minh Khoi
2 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
Trang 3INTRODUCTION
1 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 do 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
Trang 4apply 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”
2 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
Trang 5the 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
3 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
4 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
5 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
6 New contributions
6.1 In theory: Systemise the interrelationship between the theory
Trang 6of 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
7 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)
8 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
Trang 7the same as a larger segment containing it as shown in Figure 0.1
- 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
Fig 01 Example of the Fractals in mathematics and nature
Trang 8CHAPTER 1 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
Trang 9Despite 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
Trang 10extraordinary 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
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 do 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 Fig 1.1 Illustrations of modern architecture with an application of Fractal geometry at a simple level and a higher level
Trang 11architecture
Although the understanding of Fractal geometry is currently still limited, many architects working in Vietnam, both home architects and foreign architects, are influenced by the self-similarity designs and modular trends in architecture of the digital age which is closely related to Fractal architecture Therefore, many buildings - either technologically or ecologically inspired - are highly fractalised
Fig 1.2 Examples of Fractal geometry in ancient and modern
Vietnamese architecture 1.3 OVERVIEW OF RELEVANT STUDIES
In architecture, both theoretically and academically, Carl Bovill - Associate Professor at the University of Maryland (USA) is the first author to write the book “Application of Fractal geometry to Architecture and Design”, which immensely focused on architectural criticism Later, many scholars such as James Harris, Iasef Rian, etc., studied the application of Fractal geometry in association with specific types of buildings or with general points of view
In Vietnam, “Fractal” is still a relatively new concept and has only been primarily mentioned in mathematics In architectural theory, the notion of Fractal geometry remains as an unexplored question 1.4 GENERAL COMMENTS AND RESEARCH QUESTIONS
Trang 121.4.1 General comment
Applying Fractal geometry to architectural composition in Vietnam is
a new topic The so-called direct applications or expressions of Fractal geometry which could be seen in many buildings are demonstrations
of the great potential for its application to architecture, especially in the era of the revolution 4.0
1.4.2 Research questions
- What is the relationship between the theory of Fractals shaping and the theory of architectural composition? May Fractal shaping and its variations be compatible with architectural composition?
- How can architects and researchers apply Fractal geometry to architectural design? Which gaps, in theory, should be filled and which issues need to be generalised, systematised and consolidated? What should be emphasised in the application in Vietnam?
- Which building types in Vietnam may be chosen first for the application of Fractal geometry? At which stage? For which elements? How to apply this concept in Vietnam and which projects should be selected as examples? How can the built form design take shape in the process and how should it be combined with graphic design?
CHAPTER 2 SCIENTIFIC BASES FOR THE APPLICATION OF
FRACTAL GEOMETRY TO ARCHITECTURAL
COMPOSITION IN VIETNAM 2.1 THEORETICAL BASES
2.1.1 Theoretical bases of Fractal composition
2.1.1.1 Fractal shaping in view of “initiator and generator”
An initiator: is a starting shape for Fractal shaping to continue
A generator: a is set of similar shapes of an initiator to be used in
Trang 13replace of that initiator
Level: every time when the initiators are replaced by the generators, a level has been set up
2.1.1.2 Characteristics of Fractal composition
- Each Fractal composition is an irregular shape;
- Self-similarity can continue on various scales;
- Supersize shape with an odd number of dimensions
2.1.1.3 Some basic Fractal compositions
Fig 2.1 Example of shaping Sierpinski triangles and variations by
means of “initiator and generator”
Intiatator
Step 0 Step 1 Random variant
Step 1 with randomness Step 2 – repetition of rule Step 2 with randomness
Trang 14b 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