The Study Of Architectural Design Based On Fractal Geometric Theory

In the influence of complexity theory,Fractal,as a non-linear geometry,reveals the appearance and operation rules of the real world,and has the ability of accurately quantify the complexity of the system,so,it has been widely applied into many disciplines in recent decades.Especially in architectural field,which closely bounded with geometry research,fractal geometry can be regarded as a guidance system of forms and rules,greatly expands the scope of architectural design and its related theories.However,the combination of fractal and architecture is still at the preliminary stage,most applications of fractal in the field of architecture are limited to intuitive imitation in appearance and arbitrary use of relative algorithms,the deeper philosophy between these two fields needs to be further developed.Therefore,in the perspective of Architecture,this dissertation extracts and optimizes the Morphological Mechanism,Algorithmic Logic,and Fractal Dimension in fractal geometric thoery,to make them more suitable for the field of architectural design.Deeply exploring the diverse applications of fractal in architecture,and providing more possibilities in the future design works.This thesis first analyzed the influence of different geometry in the development history of architecture.Which includes: the fundamental role of the Euclidean Geometry to architectural design,the paradigm changes in architectural design along with the expanding of the geometry theory(Non-Euclidean Geometry,Topological geometry),then the promising concept of the Fractal Geometry is derived in the architectural design.It can be known from the analysis that the influence of a geometry on architecture mostly present,from superficial appearance to deep thinking,from qualitative to quantitative,as the aspect of design morphology,design principle,and design quantification.Based on which,the following research subsequentially focused on the application of fractal geometry in architectural design in three aspects:‘Morphological Mechanism’,‘Algorithmic Logic’ and ‘Fractal Dimension’.(1)In the aspect of Morphological Mechanism,the three constructive elements are extracted from self-similarity in fractal and applied to architectural design.Starting from the self-similarity,the most essential morphological feature of the fractal,it has been analyzed and deconstructed into three constructive elements: ‘initial form –generative logic – iterative loop’,which subsequently have been applied for generating and analyzing the design strategy of architectural surfaces,spaces,and structures.The result showed that the three constructive elements of self-similar can be used as manageable parameters to generate diverse results more easily and quickly.It can be regarded as a design constructive method that break the limits of simple intuitive imitation of fractal in design,enrich the design diagram from the perspective of generative strategy.(2)In the aspect of Algorithmic Logic,the deeper rules of L-system and IFS algorithm are extracted,and further applied as design methods into the analysis and practice of architecture;This chapter discussed the relative algorithms of fractal,L-system and Iterated Function System(IFS),in the order of ‘algorithm analysis – rule extraction – design application– method summary’.To be specific,through the analysis of L-system,the design method,morphological grammar,is extracted,and then analyzed its application in design process step by step.With a design program of coffee shop,the design method of the morphological grammar is further practiced.on the other hand,through the analysis of the IFS,the design method,the strategy of ‘iterative-feedback’ is extracted,and then classified its application in design process.With a design program of the War Museum,the strategy of ‘iterative-feedback’ in design had been further practiced.In conclusion,compare with the arbitrary use of the fractal algorithm,the design methods analyzed and extracted from it can help architects cultivate the logic thinking of design,and pay more attention to control the design process.(3)In the aspect of Fractal Dimension,considering the characteristics of architectural design,the optimized algorithms of fractal dimension,which includes 1-2 dimension and 2-3 dimension,are programmed and applied to the quantitative research of buildings in various research situations.Based on the feature of continuously covering the integer and decimals of fractal dimension,this chapter discussed the architectural quantitation in 1-2,2-3 fractal dimension respectively,and in the order of ‘algorithm introduction – algorithm optimization – algorithm application’.Specifically,the range of 1-2 fractal dimension measures the visual complexity of the building’s image.Based on the box-counting algorithm,the parameter ‘observation distance’ has been introduced into the optimized algorithms according to the architectural characteristics,and the ‘fractal dimension trend’,which resulted from the optimized algorithms,presents the dynamic process of the observer’s receptions of the visual information of a building while moving.Subsequently,the optimized algorithm had been applied into the quantitative analysis of building’s visual complexity map,the tour experience of Shizi Garden in Suzhou,and the spatial experience in the Forbidden City.In the range of 2-3 fractal dimension,the spatial complexity of building(s)had been investigated.Base on the optimized 3-dimensional box-counting algorithm,the greater scales of a building or urban buildings are considered,so,this chapter proposed to modify the setting of the box size,and an efficient computation method using geometric analysis in the optimized algorithms.Which has been used to further measure the spatial complexity of 6 buildings and 5urban buildings.As a conclusion,it is clear that the fractal dimension can be used as an accurate quantitative tool to explore and analyze the digital features hiding behind the architecture.There are three innovations in the research of architectural design based on fractal geometry theory.To sum up,the ‘Morphological Mechanism’,‘Algorithmic Logic’ and ‘Fractal Dimension’ in the theory of fractal geometry can correspondingly have guiding significance for the aspect of design morphology,design principle,and design quantification.Meanwhile,fractal is also a rigorous mathematical science,whose combination with architecture needs to be extracted and optimized to be further expanded its application in architectural field.