Zhang Yijie  Doctorand

Tang Zhong  Senior Engineer

Tongji University, Shanghai, China,



Abstract: After the research of “The generate method of Multi-storey Chinese Pagodas”(GA2002 Page26.1), we go on to find the usage of GA in the design of Chinese pagodas. For Chinese pagodas are traditional buildings, not all of modern designer can design it with traditional way. We try to find a modern way for modern designer to design traditional Chinese pagodas with GA in this paper.

Keywords: generative, pagoda, design, Chinese, pagoda



This religion took shape in about 500BC in ancient Indian, and was soon widely propagated in the world, especially around the Eastern-Asia. During the first century AD it got into the territory of the Han Dynasty, then in the following several centuries it had been widely spread around the Eastern-Asia, including the Korea Peninsula and Japanese islands. With time going on, it had been one of the most important parts of the Eastern-Asia culture.

Buddhism is a religion of image, that is to say, it is preached through images. Thus innumerable images of Buddha as well as Buddhism pagodas had been built up, which monks and laymen can pay their homage to. Through the whole Eastern-Asia area and during the history with Buddhism in this area, Buddhism pagodas had been constantly erected under Buddhists’ religious zeal. Thus Buddhism pagoda gradually became one of the most important architecture types in this area, and the constructing technology of this kind of building gradually became mature.


Buddhism pagodas

As time going on, Buddhism pagoda evolved more senses beyond religious symbol, its tall, graceful and striking appearance usually made itself a mark of a city, or an important part of a scenic spot.

As a cultural symbol of Eastern-Asia, Buddhism pagodas are still popular today. Many famous Buddhism pagodas in the history had been repaired, renovated or even rebuilt; and new ones are still constantly built up because Buddhism is still well received in these areas. Furthermore the elegant, striking appearance of multistory pagoda is still admired and enjoyed by people there. This pretty appearance can be used in the new multistory building and new scenic spot too.

Pagoda today

So pagoda still has its market in Eastern-Asia. The problem is how does nowadays architects design this kind of building, with traditional appearance or with characteristics.

We know that ancient Eastern-Asian had evolved their traditional architecture system, this system included a whole set of ideas: designing, manufacturing, constructing and so on. These ideas are mature and definitely different with nowadays. And they are a little complex, so obscures to nowadays architects. This paper wants to establish a mathematical model to simulate this kind of building. The references in the model can be achieved from these numerous relics. Then we can make a communicable computer program to help architects to design nowadays pagodas.

What is the experiment?

As we talked above, the aim is to establish a generative project for nowadays Eastern-Asia Buddhism pagodas designing. Thus the final appearance of the building must have the traditional disposition. So this experiment is an exploration to probe the realities of historic research. Furthermore this experiment puts forward an idea of how to abstract historic spirit and then bestow them on nowadays creations.

1.     Typical Model of Buddhism Pagodas’ Shape

As we had discussed in the previous paper, in Eastern-Asia people had evolved four main types of Buddhism pagoda, and the multistory ones(楼阁塔) and close-eaves ones(密檐塔)occupy a great part of these. Even more these two kinds are better received in nowadays new-pagoda designing. So this paper will concentrate on these two types.

And as we had talked about in the previous paper, every traditional Eastern-Asia pagoda has four parts: underground palace, platform, body and steeple. We know that the body is the main part of the appearance, so this paper will focus on the shape of the body. The other three parts will be discussed in future research.

Because this paper pays close attention to the body shape of the pagoda, regardless the religious themes and other details, we will just focus on the rough shape of the body, and only on the geometric figure.

Then looking into all traditional multistory pagodas(楼阁塔) and close-eave pagodas(密檐塔), we can find out that though in details they are definitely different from each other but from geometric angles they are typically the same. They are all central symmetry platforms, and are constituted with several such kinds of platforms. The geometric model can be a series of similar platforms, which are pilled up on each other with size diminished while height increased. Another feature is that the planes of these platforms are all regular polygons while the number of edges is even number, in Chinese philosophy this kind of number resembles YIN(阴), the earth, low, muddy and things like these. While the layers must be odd number, which resembles YANG(阳), the heaven, high, clear and things like these.

2.     Steps of Generative Designing

From above analyzing, we can easily establish a typical model of pagoda. Then we should consider how to undergoing a nowadays pagoda designing. From our experiences, it can be separated into three main steps:

Firstly, we decide the scale and type.

Secondly, we decide the rough outline.

Thirdly, we decided the details.

As we had discussed before, this paper will just focus on the first two steps. Lets deepen the study now.

The first step: deciding the scale and type

When we begin a design, firstly we should make sure the location, then deciding the scale and type. We used to describe the scale with two references: H (the height of the pagoda), R1, R2 (the radiuses of the circumscribed circle at the bottom of the lowest platform (R1) and that at the top of the top platform (R2)). We describe the type with two references. One is S (the shape reference of the pagoda. For example, we can define S=1 standing for multistory pagoda, S=2 standing for close-eave pagoda.) The other reference of type is N (refers to the number of the stories, as we had discussed before it should be an odd number).

When we input the certain numerical values of these references, then we can acquire a rough shape of a pagoda: it will be a frustum of a cone. We can judge the rough shape according the nearby environment.

Then we go deep into the second step.

The second step: deciding the rough outline of the body.

As we had discussed above, the body is not a simple cone, it is constituted with a series of piling-up similar frustums of platform whose flat form is regular polygon. Thus we should go into details of the outline of the body. We looked back into all traditional multistory pagodas(楼阁塔) and close-eave pagodas(密檐塔), easily  we can find out that the outline can be simply sorted into two rough kinds: One is nearly a line, the other a kind of parabola. Thus we simply decide two main types of the outline:

Hi=f (Ri)=a*Ri+b----------------------------------------when the outline is nearly a line.

Hi=f (Ri2)=a’*Ri2+b’---------------------------------when the outline is nearly a parabola.

Hi: the height of the outline of the No. i story

Ri: the radiuses of the circumscribed circle of the outline of the No. i story

a, b, a’, b’: constants decided by the designer. The shape of the outline has relationship with these constants. But we can bestow historic characteristics into the shape through give certain scopes of these constants, and the scopes are decided on the basis of analyzing all the traditional pagodas.

When we input the certain numerical values of these references, then we can acquire a rough shape of a pagoda: it will be a series of piling-up similar frustums of platform whose flat form is regular polygon. We can judge the rough shape according the nearby environment.

Then we go deep into the third step. This will be discussed in future research.

3.Data Base

To make the project be generative and with ground, we must analyze all pagodas built during ancient in the Eastern-Asia area first. To make it more useful, we suggest that analyses should be undergoing after sorting all historic pagodas, and undergoing according to the classifications. The standards for classifying can be eras, districts, types and so on. Eras can be classified according to the Chinese historic periods. Districts can be sorted according to the different local architectural styles. Types refer to multistory pagoda type and close-eave pagoda type; maybe in future we can spread our research to the other types.

Through the above analyses we can acquire a series of references or scopes of constants, these have relationship with the era, local architectural style and type as well, they come from history and go into future. Thus we can establish a database of the Eastern-Asia pagodas, this will be the base of the generative project. Then architects can design pagodas with the help of this generative project. With the database the final shape of the pagoda outline will have some traditional characteristics even the designer has poor knowledge about the traditional architecture. He can create a pagoda with pure Tang Dynastic feature; even the features were only popular in a small area, as if he is an architect with profound traditional architectural accomplishments. Or he can create some compromise pagodas.

4.How to Use?

Then we should set up the project with the help of programmer. They can design an easygoing program on the base of the mathematical model and the database we had discussed above.

For architects, they just input some mathematical values then the program will generate a three-dimension model, which is readily for designers to judge. So it is very easy to communicate with the program.