The Influence Of Mathematics On The Evolution Of Architectural Morphology

Under the background of the increasingly complex architectural morphology,the influence of mathematics on the formation of architectural morphology is becoming increasingly significant.The ultimate purpose of this paper is to clarify the way and principle of mathematics acting on the generating of architectural morphology and explore the evolution law of architectural morpholoy in the future.This paper attempts to extract the important influence on the evolution of architectural morphology from the mathematical theory of huge system,and then prove the law contained in it by empirical research.According to the time division of mathematical history,there are three important periods in which mathematics is closely related to the architectural morphology:In the period of Elementary Mathematics(6th century BC-16 th century),static and balanced European geometry provided design methods and modeling rules for Western classical architectural form design.In the second chapter,through literature research,the formation mechanism of architectural morphology under the influence of Euclidean geometry is clarified.This paper puts forward the Euclidean geometric tradition of classical architecture based on the deduction of ruler and gauge,and systematically combs the occurrence,continuation and specific ways of its effect on architectural design through specific cases.On this basis,the Euclidean tradition based on geometric deduction and the Vitruvius Pythagorean tradition based on arithmetic are further distinguished.Among them,Euclidean geometry deduced by ruler and gauge is an important method of communication between architects and craftsmen.It integrates architectural design,structural stress and construction together,which is an important principle for the formation of western architectural forms.During the period of variable Mathematics(17th century-18 th century),the focus of mathematics research turned to the motion in space.Through promoting the development of structural mechanics,analytic geometry and calculus have an impact on architectural morphology.The combination of them makes the fit of architectural form and force more scientific and reliable.Its direct influence on the architectural form is embodied in the introduction of various non-circular function curves and ruled surfaces into the architectural form design,and its indirect influence on the architectural morphology is the form-finding design based on structural optimization assisted by computer technology.In chapter three,the author tries to design with the Bi-directional Evolutionary Structural Optimization which based on the finite element theory and Rhino Vault plug-in based on graphic statics.In the modern mathematics period(1820 to now),non European geometry has created a new concept of space.High dimension,bending,topology transformation,random,self similarity,self-organization,complexity and so on become new elements to describe space.Under the support of parametric design technology,the generation rules of architectural form are more complex.The application of space curved surface promotes the architectural form from Euclidean space to non Euclidean space.Chapter four introduces the core concept of topology “manifold”,which explains the internal relationship between the change of architectural space-time concept and the three-dimensional free space surface from the perspective of mathematics specialty,and predicts the realization of architectural Data-Forming through manifold learning in the future.Chapter five introduces the application of fractal theory in the formation of architectural morphology.Tyson polyhedron,L-system,cellular automata,seepage and further renormalization are tried to be applied to the three-dimensional space design and landscape design of buildings.Chapter six studies the calculation of the complexity of building surface by using the 3D box-counting dimension.By setting the weight parameters,the 3D box-counting dimension is more significant and accurate in the calculation of the complexity of the building surface.It is found that the influence of mathematics on the evolution of architectural form includes two aspects: one is that the change of mathematical space concept guides the evolution trend of architectural form: from static to moving,from straight to curved,from simple to complex.The second is that mathematics provides a specific way to generate architectural morphology: Geometric deduction of ruler and gauge and computer algorithm generation The generation method of ruler and gauge deduction is based on the Euclidean geometry;the algorithm generation is based on computer technology,and most of the mathematical theories can be transformed into algorithms for building form generation,including the architectural morpology dominated by structure,by form and by data.The 3D Box-counting dimension can give an accurate quantitative value of the complexity of the architectural surface.The space filling ability of the architectural form with the surface is significantly higher than that of the planar architectural form,and that of the spatial surface is higher than that of the ruled surface.