# Explore the application of fractal geometry in architectural design

Abstract: fractal geometry is an important part of the nonlinear science, mathematics, mathematical thinking in building design has been fully applied, the paper first gives some important features of the related concepts of fractal geometry and fractal geometry has Then, fractal science applications in building design exploration analysis of its specific applications in the architectural design Finally, the prospect of fractal geometry in architectural design.

Keywords: fractal geometry, architecture design, application analysis With the rapid development of China's economic construction, the aesthetic ideas of building has also undergone a lot of changes, no longer simply focus on the practical value of the building, and pay more attention to its visual beauty. Fractal geometry applied in many aspects of building design, example, epidermal fractal fractal body detailed structure of fractal and so on.

## A related concept of fractal geometry and characteristics of

(A) points to the concept of morphological as nonlinear science, one of the important concepts of fractal geometry, "fractal" meaning literally "broken" and "irregular". Fractal theory as a branch of modern mathematics, in essence, to elaborate a new world outlook and methodology.

## (B) the characteristics of fractal geometry

A fractal geometric fact have been present in the natural being, such as: the famous KOCH curve gives a straight line segment, the middle of the two halves of these segments to replace the two sides of the equilateral triangle, and in the new graphics, each third portion of the straight segment of the graph continues with the two edges of the triangle to be replaced, repeated operation, KOCH curve is formed, constitute a major use of this curve learn the principles of fractal .2 fractal geometry, the main object of study is the fine structure of the self-similar nature of the infinite, the natural shape of things as unlimited nesting level logic structure, and does not change because of the scale of change their similarity.

## Fractal learned in building design specific applications

Architectural design is good or bad is not only related to the appearance of the building, is more related to the overall security of the building, the architectural design is a very particular about the scientific research work. Fractal science as a field of study of mathematics, its scientific is no doubt a wide range of applications in building design, the following specific about the architectural design.

(A) of fractal geometry in building epidermal design applications in this regard, the Beijing Olympic swimming stadium, Water Cube is very representative, the Water Cube design with its simple and elegant image for the majority of foreign tourists left deep impression, its design concept from Wearie Phelan unlimited equal volume of soap bubbles array geometry problem of answers. First, the need to produce a greater Wearie Phelan foam structure array compared with the building and then, the the generator matrix to a vector for the center for rotation, and finally the foam structure in the external space and the internal space of the building shear continues after the rest of the sector as the construction of the roof and the wall constitutes this way, the basic " Water Cube "declared completed, the foam structure of a building carried out in accordance with the law of the three orthogonal axes repeated to build, to form a whole building model. fractal concept in the wall construction and roof design of the Water Cube has been fully reflected in the application of its basic structure is the use of a rotation and cutting them achieve, gives the impression that is the whole concept of a strong and very subtle. posted in the free papers Download Center http:// eng.hi138.com (b) the application of fractal design school in the "body" of the building
1 building three-dimensional fractal design, building 3D fractal usually be called is "body" sub-shaped, is the construction of the "body" through proper rotation, scaling, and linear translation and other related fractal operation, to a simple unit change reasonable for many similar or identical elements, and these elements are grouped together, and thus form a higher level of particle unit, after completion of the work, to proceed with a new round of translation, and continuously repeating this procedure, the final formed a lot of wireless multi-level unit combination .2. the Peter Eisenman scale scaling famous avant-garde architecture in the United States residential Peter Eisenman designed the first formal application of complexity science in the field of architectural design, he takes full advantage of the principle of fractal geometry scaling, the use of three-dimensional 'L' shaped complex rotational structure into the volume of the building, is the architect's first awareness of the use of fractal geometry to the performance of the building complex and diverse.

(C) the design of complex-shaped design architect Zhen Fumihiko spiral Building (Sprial Building, 1985), as a "square" building "generator" scaling method to construct a series of different sized square and for the building which the fractal structure of the building, and, in addition to the use of the fractal dimension theory, also into a lot of heterogeneous elements, orderly splicing mixed fully reflect between the buildings and the city between the whole and the parts, between chaos and order isomorphic principle architect claimed that: "the spiral building construction design concept with the idea of ​​the city there are a lot of similarities, and want to take their complete dedication, so that people at random be cut completely dismembered reacquire life. "designers is to have the complex diversity of the building itself to reflect the complexity and diversity of the society.

, Fractal geometry in architectural design development outlook since the twenties of the last century, the world architect who constantly seek breakthrough architectural design and want to be able to carry out reform and innovation of the original architectural language , so there is a qualitative leap. fractal theory in modern mathematics, it has "self-similarity", "scale", "scale level", "scale transformation" characteristics, caused by the scholars in the field of architectural design great concern in building design and constantly be a bold attempt and achieved very satisfactory results, the design of the buildings more close to nature, and in harmony with the surrounding environment. meet people's aesthetic ideas. , after all, a shorter development time, many aspects need to further explore and try, must recognize domestic economic construction and development situation and the community in their level of awareness of the achievements at the same time, can not be solely their own ideas, casual design, or design works once can not coordinate with the social environment, will have adverse social impact, this aspect of the design development will also adversely affect the operability of the design, therefore, we should pay attention to play its maximum design advantages of today's era, new forms, new thinking to create superior growth environment, especially in today's construction market is in a very active period, to firmly grasp the opportunity, the quality of architectural design leap struggle.

## References:

[1] Gu red male, Zhanju Cong. Fractal geometry in architectural design applications [J]. Sichuan building, 2011,01
[2] Lin Qiu reached from "Nature as Teacher" to "algorithm naturally" - fractal law in architectural design, the use of [J]. Fujian architecture, 2010/11 Links to free papers Download Center http://www.hi138 . com