A Formal Approach to the Study of the Description of Chinese Lattice
Yu Wu
A Formal Approach to the Study of the Description of Chinese Lattice
Yu Wu
School of Journalism and Communication, Zhongnan University of Economics and Law,
Wuhan, 430073, China,[email protected]
Abstract
Chinese lattice can be treated as patterns that can be widely used as design elements in modern
design. However, the lack of formal descriptions of lattice makes its application process very
inefficient. In this study, we utilize shape grammar as a formal approach to describe the Chinese
lattice and give a complete definition for it. The formal description of Chinese lattice can clarify their
unique style and greatly improve the efficiency of applying them in design practice.
Keywords: Shape Grammar, Pattern, Symmetry, Culture, Evolution
1. Introduction
Chinese lattice is made out of wood, a material that is not long lasting. However, as patterns
with cultural meaning, they can be found in the grave from the Chou dynasty, which are about
three thousand years before. In addition, they can be found in patterns on grave brick, pottery,
clay house, painting and so on.
From the Han dynasty (206 B.C. to 220 A.D.) to the Qing dynasty (1644 A.D. to 1911 A.D.),
lattice evolved from very simple one only with vertical bars to very sophisticated one with
patterns and ornaments. Chinese lattice reached its culmination in variety and design at Ming
dynasty (1368 A.D. to 1644 A.D.). As an important component of Chinese architecture, lattice
is always treated as patterns through which convey the ideology of the users, most of them are
the literati and officialdom in ancient China.
Chinese lattice designs are a rich source of interesting geometric forms and shape grammar
has been used as a means to describe the designs of the Chinese lattice. Daniel Sheets Dye
catalogued various Chinese lattice designs constructed between 1000 B.C. and 1900 A.D. into
twenty six general types in his classic work “A Grammar of Chinese Lattice”.
Chinese lattice is the pattern with cultural meaning, so content analysis is very suitable to
examine them. As the special artifact that recorded the human behavior, patterns can show the
unique identity of certain styles through the content analysis. Moreover, combining with formal
approach, we can examine the commonalities and the evolution process of the patterns in a
precise and intuitive way [1, 2].
Shape grammar, as a formal approach to content analysis, is a production system that
generates and analyzes designs according to sets of shape rules [3]. Shape grammar has already
been used to define the languages of designs such as ornamental art [4, 5], architecture [6], and
Islamic patterns [7].
The rest of the paper is organized as follows: Section 2 reviews the literature on the problem
of representing lattice in a formal way. Section 3 illustrates our methodology for developing a
complete language for Chinese lattice. In Section 4 and 5, the generative language and pruning
language for lattice are presented respectively. Section 6 proposes a new way to represent the
special case of Chinese lattice. Section 7 provides conclusions of this paper.
2. Related works
2.1 The classification of Chinese lattice
Chinese lattice has the same history as Chinese architecture. Chinese lattice is made out of
wood, so it is impossible to find the real wooden lattice that existed three thousand years before.
Fortunately, in the Ming and Qing dynasty, there are left examples of real wooden lattice that
International Journal of Digital Content Technology and its Applications(JDCTA)
Volume6,Number13,July 2012
doi:10.4156/jdcta.vol6.issue13.49
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A Formal Approach to the Study of the Description of Chinese Lattice
Yu Wu
can be found in the ancient architectures. Lattice reached its culmination in variety and design
at Ming dynasty.
An efficient and precise classification is very critical to describe the lattice in a formal way.
Daniel Sheets Dye [8] made drawings of three thousand Chinese lattice from the buildings in
Chengdu and in the around area. According to their visual features, Dye classified them into
twenty seven groups. Some Chinese lattice designs in Dye’s Grammar are regular patterns and
some are irregular designs, like “ice-rays”. However, his classification is not precise and the
groups overlap frequently.
To be more precise, some researchers based on the mathematical foundations of symmetry to
examine the planar patterns, such as Chinese lattice. Claire Horne presented a classical
approach to the symmetry of planar patterns based on the crystallographic approach [9].
Majewski and Wang [10, 11] then presented an algorithmic approach to the creation of Chinese
lattice patterns and representation of the seventeen types of plane symmetry groups in these
patterns (Figure 1).
Figure 1. Fourteen Types of Symmetry found in Chinese Lattice
2.2 Shape grammar
Shape grammar has been used in many studies of languages of designs and their purpose is to
elucidate the languages by articulating complete generative definitions of those languages [12].
In recent years, shape grammar has been used as a means to explain the designs of the Chinese
lattice. Most of the Chinese lattice has a clearly observable periodic or regular structure that can
be straightforwardly generated by simple shape grammar [13].
As Stiny and Mitchell [14] mentioned that a complete definition for a style should specify all
and only the designs in the language. They proposed three criteria for evaluating a
characterization of a language of designs:
It should specify new designs in the language;
It should evaluate whether a newly obtained design is a member of the language; and
It should explain the perceived likeness of the designs.
2.3 Formal approach to describe a Chinese lattice
Stiny demonstrated that shape grammar can generate most of the Chinese lattice designs in a
very simple and intuitively compelling way (Figure 2). When Stiny defined the ice-ray designs,
he also tried to investigate the conventions used to construct Chinese ice-ray designs and
defines the parametric shape grammar that can describe the making process. The mentioned
researches about Chinese lattice designs all follow the design intention described in Dye’s book
and their shape grammar rules cannot cover certain irregular ice-ray designs.
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A Formal Approach to the Study of the Description of Chinese Lattice
Yu Wu
Figure 2. Stiny's Rules for Regular Lattice
3. Methodology
When we think about making a complete definition, there are two basic possibilities. The
first is a partial enumeration, partial enumeration because we have only but not all designs in
the language. The other possibility is a partial generative definition, partial because it does not
specify any designs in the language (not all), specifies some designs not in the language (not
only), or both (not all and not only).
In this research, we try to formally describe a Chinese lattice using shape grammar and
present a complete definition for it. In other words, our purpose is to create a complete
generative definition (all and not only) for Chinese lattice by using shape grammar.
Our research is based on the Majewski and Wang’s classification of Chinese lattice, which
can provide a framework to describe Chinese lattice formally.
More specifically, our approach can be divided into two steps. The first step is to utilize the
seventeen two-dimensional symmetries as the framework to get the all but not only a definition
for Chinese lattice. By categorizing and formally describing the existing Chinese lattice, we can
get the shape grammar that can generate all and not only Chinese lattice. The second step focus
on the pruning issues, such as cultural consideration. We try to get the language that can prune
the non-Chinese lattice. Finally, we deal with the special case in Chinese lattice, irregular iceray lattice.
4. Formal language for Chinese lattice
By utilizing the seventeen two-dimensional symmetries, we can get the language that can
generate all but not only Chinese lattice.
4.1 The structure of Chinese lattice
Shape grammar is descriptive enough to reveal intrinsic regularities in designs, and can assist
in understanding commonalities and differences between two different styles. However, the
application of shape grammar in the analysis of cultural artifacts is not sufficiently developed
for deconstructing and describing the artifacts according to their symbolic memes. The
deconstruction of an artifact into meaningful components is necessary to define counterparts
that can be compared with other artifacts in different styles. Moreover, some researchers believe
shapes and patterns can be deconstructed using a hierarchical classification of shape rules. In
this research, shape grammar needs a hierarchy of shape rules to deconstruct Chinese lattice
more systematically.
We propose a formal strategy for the hierarchical deconstruction of Chinese lattice to its
symbolic memes using shape grammar to clarify the evolutionary process and commonality of
patterns.
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A Formal Approach to the Study of the Description of Chinese Lattice
Yu Wu
Generally, a Chinese lattice (Figure 3 a) can be divided into two parts: the global structure
(Figure 3 b) and local structure (Figure 3 c).
a
b
c
Figure 3. A Chinese Lattice and Its Global and Local Structure
4.2 The classification of global structure
There are two different global structures for Chinese lattice. One is the orthorhombic bars
(Figure 4a) and another is the heterotrophic bars with sixty degrees (Figure 4b).
a
b
Figure 4. The Global Structure of Chinese Lattice
We can easily categorize the fourteen types that mentioned before into these two different
global structures. Ten of the fourteen types can be categorized into the orthorhombic structure,
which is mostly seen in the ordinary architectures (Figure 5).
Figure 5. The Chinese Lattice with Orthorhombic Structure
The second global structure, heterotrophic structure, is for particular architectures such as
palace and temple. We can find four out of fourteen belong to the heterotrophic. (Figure 6)
Figure 6. The Chinese Lattice with Heterotrophic Structure
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A Formal Approach to the Study of the Description of Chinese Lattice
Yu Wu
The classification of the global structure of the Chinese lattice can provide a brief
classification of Chinese lattice. Furthermore, the examination of evolution process inside
certain global structures will be much easier. In the future work, we will describe the evolution
process of the global structure using shape grammar and examine the related historical
background.
4.3 Local structures for Chinese lattice
Comparing with global structure, the local structure of Chinese lattice is more complex and
has more varieties. In some sense, lattice can be comprehended in the way that global structure
provides the framework for the local structure to fill with.
Generally, the local structure of lattice can be derived from cultural consideration, from
global structure and from the emerging shape (Figure 7). There are many symbols like Swastika
utilized in Chinese lattice. Moreover, local structure can be also derived from other sources.
Figure 7. Local Structures of Chinese Lattice
4.4 Pruning language for Chinese lattice
By using some pruning issues, such as cultural consideration, we can get the language which
can prune the lattice that does not belong to Chinese lattice.
Many issues can be utilized to prune the generated outcomes of generative rules. A
systematic method to consider these issues is very critical for the completeness of definition of
Chinese lattice.
The pruning issues can be derived from the cultural consideration or taboos that root in
Chinese culture. Some may be the formal constraints that keep the lattice in the well-organized
way.
To put the pruning issues into practice, we need transfer them into shape rules. For the local
structure we examined in the previous section, we can compare it with the existing local
structures and summarize the difference between them and get the rules as follows.
1) The line should have two points of intersection on the edge;
2) The point of intersection should be on the 1/2, 1/3, 1/4, or 1/5 of the edge.
5. Generative language for irregular ice-ray lattice
Through section 4, we can describe almost all the lattice in a formal way. In this section, we
try to figure out the way to describe the irregular ice-ray lattice.
5.1 Design intention embedded in the Chinese lattice
We choose the Chinese lattice shown in Figure 8 as an example to find the design intention
embedded in it. At first, we define the shape rules and the corresponding lowest-level
constituent that can generate the lattice pattern. Then, the meaning of lowest-level constituents
will be examined to trace the design intention embedded in the lattice window.
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A Formal Approach to the Study of the Description of Chinese Lattice
Yu Wu
Figure 8. Two Constituents with Cultural Hints
The chosen window can be categorized into checkerboard design mentioned by Stiny. Stiny
used two schemas for the checkerboard design. The First one is x >x + t (x) to produce the
checkerboard pattern and the second is x>div (x) to inscribe the given motif and divide squares.
The chosen window can be generated by using stiny’s schemas if we choose the motifs as
shown in the Figure 2.
It is very interesting to find that the chosen window can be generated by two different motifs
respectively. But this raises the problem. Which one can represent the design intention
embedded in the lattice window?
This problem raises when you calculate with shape. When we use shape grammar to calculate
with shape, we divide the shape into the lowest-level constituents, which are the symbols that
are necessary for syntax. But for a specific shape, we can segment shape into the lowest-level
constituents in many different ways. This causes the questions like which way of segmenting
shapes into constituents makes the most sense in terms of what we want to calculate? Which
analysis works best? Stiny suggested that we can dynamically change the constituent while we
make the rules until we find the suitable one that can help calculate the shape. Stiny illustrated
the problem about decision making when he faced several choices to segment the shape. He
thought it was critical to choose the suitable way to divide shape into the lowest-level
constituents, especially when someone is dealing with the design problem. In design, what you
want to calculate may not be evident before you start. You may not know until you’re finished.
5.2 Cultural information embedded in the pattern
If we treat the window as a checkerboard design, the motif becomes the lowest-level
constituent to calculate, and we may miss the information in it because it is merely considered
as a shape. Design is an intentional activity and design intention will be influenced by the
cultural context inevitably. While many cultures create designs with geometric patterns, each
has distinct motifs and symmetries. The pattern of Chinese lattice may contain some cultural
information which influenced the design intention. As Dye described ice-ray in his book A
Grammar of Chinese Lattice.
I have described it as the result of a molecular strain in shrinking or breaking, but more recent
observations and photographs seem to prove that it is a conventionalization of ice-formation which
has become traditional.
Ice-ray lattice is not merely the imitation of natural phenomenon, it has become the pattern
which contains some cultural information and design intention. In this study, we propose a new
way to select the lowest-level constituent for calculation. We utilize the cultural hints that are
related to a Chinese lattice to select the lowest-level constituent. In doing so, we may find out
the embedded design intention and describe it by shape rules.
In the Chinese traditional building of Huizhou region, we can find the special pattern which
consists of a hexagon in the center named “XuanJi” in Chinese ornamental pattern and the
“Human figure” composed of every two bars around the hexagon.
Based on the understanding of the ice-ray pattern, we propose a new perspective to look at
the design intention of Chinese lattice design. The lowest-level constituent of the window
should be the “Human figure” and when the Chinese artisan makes the windows, the design
intention is to embed the “Human figure” in it. And it is not hard for us to find the “Human
figure” in the previous motifs (Figure 9).
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A Formal Approach to the Study of the Description of Chinese Lattice
Yu Wu
Figure 9. The “Human figure” in Motifs
To define the new shape rules for the lattice design, we should consider the “Human figure”
as the lowest-level constituent and add one more rule to describe the process form “Human
figure” to the previous “lowest-level constituent”.
5.3 New grammar for ice-ray
We will develop the new shape rules for the ice-ray design and use them to describe the
making process of a Chinese lattice that cannot be generated by existing shape rules. Our
grammar contains two shape rules:
1. Put a hexagon in the centre;
2. Create “Human figure” by adding a bar on existing one.
For the rule1, the hexagon can be replaced by a triangle and the aim of this rule is to create a
center in the window pattern. For the rule2, the length and angle of the added bars vary in
different situations.
The difference between our rules and Stiny’s is on the understanding of the design intention
embedded in the ice-ray. When Stiny examined the ice-ray designs, he followed Dye’s
understanding of the lattice design.
In the case of the ice-ray pattern, [the artisan] divides the whole area into large and equal light
spots, and then subdivides until he reaches the size desired; he seldom uses dividers in his work.
Stiny himself also illustrated the design intention behind the ice-ray design as the following.
One can image a Chinese artisan, summoned to a building site; bring with him tools and
implements and a collection of finely finished sticks. Shown a rectangular window frame, he is
asked to create an ice-ray lattice. He begins his design by selecting a stick of the appropriate length
and carefully attaching it between two edges of the existing rectangular frame…
What Dye and Stiny described is the making process of the ice-ray lattice. The design
intention embedded in it might vary. From the cultural hints we mentioned before, we can get a
different understanding of the same making process. We can image that the artisan’s intention is
not to divide the areas but to add a bar to create the “Human figure” and to balance and
aesthetics, he tries to keep the appropriate size.
6. Discussion
In this study, we present our formal approach to generate Chinese lattice, and provide a
complete definition for it. The formal approach to describe the Chinese lattice can help increase
the creativity in modern Chinese lattice design, not just copy original one. In the future research,
a systematic way is needed to consider cultural issues. Moreover, the pruning methods should
include not only cultural issues but also other issues such as environment and material.
7. Acknowledgment
This research is funded by the MOE (Ministry of Education in China) Project of Humanities and
Social Sciences (No. 12YJC760093).
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A Formal Approach to the Study of the Description of Chinese Lattice
Yu Wu
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