GANERATIVE DESIGN OF CHINESE PAGODAS
Zhang
Yijie Doctorand
Tang
Zhong Senior Engineer
Tongji
University, Shanghai, China, tangzzzk@online.sh.cn
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
Buddhism
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.