Tying Up the Naga: Motif Design for Lao Textile

Tying Up the Naga: Motif Design for Lao Textile L. Chidtavong, M. Winckler, H.G. Bock Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University Abstract: Motifs are a dominant component to make woven pattern beautiful and interesting, and to attract attention from people. In this paper propose a LT-TieUp module which implements mathematical symmetry and is aimed to provide operations and utility tools for motif design, particularly for design motifs of Lao textile patterns. Possible symmetry operations are at the fingertip of the designer, helping to visualize their creative work before exporting it to the purpose destination. We evaluated our method on a series of benchmarks taken from original Lao textile patterns. Index Terms: Cultural Heritage, Scientific Computing, weaving, Lao textile patterns, motif design, symmetry, applied mathematics 1. Introduction Lao traditional textiles are a symbol of being Lao. Many different weaving techniques have created a diversity of patterns, which appear on costumes and household items, mainly: traditional skirts and shawls. The uniqueness of motifs and patterns make Lao traditional textiles to become a valuable heritage of Laos. The role of textiles to Lao people and their relationship was exhibited in many literatures, Dara Kanlaya and her team [2] collected all information about Lao textiles since past to present in the title Legends in the Weaving. The historical and cultural background of the Lao-Tai was examined by Mary F.Connors [6], this exploration shown the link between their ancient traditions and their adaptation to the modern world, the author also explained what sort of textiles were woven and how they were used in daily and ritual life. A strong relationship between motifs on the Lao textiles and belief in religions were explained by Ellison Banks Findly who is a specialist in religions and Asian studies [1]. Siho and Naga reflecting a people s traditions and change [3] is another title to express the importance of the textiles to the social and spiritual life of Lao people. In scientific view, motifs and patterns of the Lao traditional textiles are applied mathematical and computational methods. The patterns are often designed as striped and rectangular patterns which are exactly the same idea as symmetry patterns in mathematical study of Frieze and Wall paper groups [4,5]. Many researchers investigated the mathematical symmetry of these groups in woven fabrics. [7] examined the use of mathematical symmetries and color symmetries in various Northern Kankana-ey fabrics of the Philippine. Similar idea in [10, 12] the authors investigated mathematical basic for patterned woven fabrics, and then specified into a particular traditional textile to find out the symmetry properties on the textile. Based on the mathematical symmetry in Frieze and Wallpaper groups, a new classification and notation for woven ornament was presented in [8] by analysis axes and centers of symmetry operations. A result of a research from Lila Lekka and Sofia Dascalopoulos [11] shown that technology plays a determinant role in the appearance of woven ornaments, their

work concentrated on analyzing motifs and symmetry characteristics of the ornamentation on traditional Greek woven textiles where the analyzing result was recorded as digital preservation in the form of a database. We can see that mathematical symmetry is a fundamental mathematics for motifs/patterns design of woven fabrics. However, only this mathematics is not enough to deal with flexible design and to develop a new suitable system for each traditional textile. As a result, in our research we introduce three modules to develop a new useful weaving system for motifs/patterns design and pattern generation. The first module is a weaving design module (LT-Weave) which is aimed to construct the structure of weaving in order to get weave drafts. A tie-up/motif design module (LT-TieUp) is aimed to support ability to create new motifs, the module contains build-in Lao traditional motifs to facilitate design task. The final module is a textile design module (LT-Design), this module is concentrated on pattern composition by importing weave drafts and assigning order s index. This publication we will cover only the LT-TieUp module where almost mathematical methods used in the module are mathematical symmetry and we are going to briefly explain a structure of Lao textile motifs in next section. 2. Analysis a structure of Lao textile motifs The most motif styles in Lao textiles are Zigzag line, diamond and mythical creature motifs. They are often designed as composite symbols. A structure of Zigzag line and diamond motifs could be constructed from the same group of symbols, then a vertical reflection is applied to the symbols in order to get the Zigzag line motifs. In contrast, the diamond motifs are produced by applying both vertical and horizontal reflections. The symbols of mythical creatures became identity motifs for Lao traditional textiles, where their design techniques could be isolated into three design areas, namely: a layout of its body, outside the body and inside the body. The bodies of the creature motifs are some styles filled by lines of atomic icons and some styles filled by other motifs. To give more understanding and realization on how motifs of Lao traditional textiles look like, we would like to explain a structure of motif based on a pattern in fig.1. On the figure, there are two kinds of motifs, a main motif and its complementary motifs. A big creature symbol is called Siho, is a dominant motif. It is a creature from myth, its body is Lion s body and its head is elephant s head. On one side, if we look around to the outside of the Siho, we would see that on along its trunk is decorated by lines of atomic icons, similar idea on along its tail also decorated by a group of reflected icon lines. On the Siho s back, there is a small Siho which carried a human on its back. Moreover, beside and surrounded its body is filled by many small iconic motifs. On another side, if we look inside the Siho s body, we would see a two-headed Naga motif in s shape, motifs of naga are the most favorite motifs of Lao textiles. We could see its design style is the same fashion as Siho motif, the naga s body is filled by atomic icon along to the layout of the body, outside is surrounded by other lines where they appear along to the naga s body and some small motifs are filled to the rest of empty areas. This example not only shows how complex on the motif s structure, but it also tells religiously meaning. It presents a combination of beliefs of two religions, shamanism and Buddhism. In shamanism s ritual, the human motif represents as a shaman s spirit, the Siho motif is considered as a creature which has supernatural power to take shaman to go to spirit

world, and the Naga motif is considered as an ancestor s spirit to protect shaman during journey. Simultaneously, Buddhists respect nagas as protectors, their patterns on textiles would protect people who are wearing them from bad lucks or bad spirits. 1.(d) 1.(b). 1.(a) 1.(c). ` Fig. 1. A dominant motif: Siho with its filling motifs. 1.(a) and 1.(b) are examples of lines of atomic icons. 1.(c) is a two headed Naga motif in S shape. 1.(d) is a small Siho motif carrying a human. However, this pattern is only one example of variety motif styles of Lao traditional textiles. Moreover, a motif of the same creature could be displayed in different sizes or filled with different complementary motifs. This makes the design very flexible, giving the designer room for his creativity and imagination, a suitable design tool is highly demanded. To deal with this flexibility, we developed a LT-TieUp module which applied mathematical and computational techniques where these technical concepts are described in detail in next section. 3. Mathematical and computational techniques in the LT-TieUp module The LT-TieUp module provides a canvas and build-in motifs which are considered as binary matrices regarding to the structure of weaving pattern. While true values indicate supplementary continuous/discontinuous wefts on top of warp threads, and false values indicate warp threads on top weft threads. Graphical features of the canvas and the build-in motifs are rectangle of cells, by default black cells indicate true values of the matrix and white cells indicate false values of the matrix (see an example feature in fig. 2). The canvas is a global design area where any creative motif must be generated on the canvas. An idea to display a motif s pattern on the canvas means to assign the true values of the motif to the canvas elements at a specific position with a condition that a motif s size must less than or equal to a size of adding area. We denote is a canvas matrix with a dimension r rows and c columns, similarly denote is a motif matrix with a dimension w rows and h columns. If, is represented as an element of and, is represented as an element of to display the motif at the start (adding) point,, the values are assigned to the bottom left elements to the top right elements of the canvas. An equation corresponds to this term is presented in equation (1):

,,,, 0, 1, 0, 1 (1) Fig. 2. A graphical feature of a canvas (size 30 x 30) and a Dok Ngam motif (size 13 x 16), the adding point is (6,12). 3.1 Atomic icons and Attachment Attachment an atomic icon along to a line is a common element that often manifested on Lao traditional textiles. The lines of icons are often used as filling motifs of a main motif, and other possible motifs could be created by icon lines, such as: the lines are group together for generating a zigzag line or diamond motifs. A line of icon means attachment an icon to a path by repetitive transforming an icon s segment along to the path. The LT-TieUp module supports this ability by constructing a built-in atomic icons archiving from analysis common Lao textile patterns. This technique helps designers to get a common line or their new created line in a few steps. Unfortunately, due to a restriction of woven pattern, there are only four possible paths to be able to generate the line of icons on the canvas. These four cases are namely, a path with slope equals to 1, slope equals to -1, slope equals to 0 and finally, a path with slope equals to infinity. The attachment starts by defining begin point and end point of a path, then defines a desired icon, its segment will be memorized, a frequency of the icon appear on the path depends on a quotient of a division between path length and icon height. Mathematical notations and its equation are presented below: We denote as a motif s height as a path s length as a number of icon appears on the path 3.2 Motif operations, 0, 0,, (2) Operating any pattern on a rectangle of cells has some limitations and it is different from operations on raster or vector images. Since motifs are elements of the canvas, operating a motif means to set up a new condition for shifting or changing values of the canvas elements. In the LT-TieUp module, we developed some utility operations which are aimed to enhance a

design task to be easier and faster. The operations would encourage users to visualize a variety of possible output patterns from an existent motif. Due to the LT-TieUp module is aimed to support motif design, so the necessary operations for transformations are only rotating and flipping. By a nature of a woven pattern, there are only three available degrees to rotate a motif on the canvas, namely: 90, 180 and 270 degrees. Simultaneously, there are only four available directions to flip a motif on the canvas, such as: flip around a vertical line, a horizontal line, a left diagonal line and a right diagonal line. Note that, the direction of rotation and flipping are clockwise directions. Mathematical notations and equations for each case are listed below: We denote: as a rotation operation in 90 degree as a rotation operation in 180 degree as a rotation operation in 270 degree as a flipping operation around a vertical line as a flipping operation around a horizontal line as a flipping operation around a left diagonal line as a flipping operation around a right diagonal line Suppose that we have a motif, and its element, 0, 1, 0, 1. is a canvas, and its element 0, 1, 0, 1,,. An equation to apply a rotation operation to the element, of the motif at the rotated point, on the canvas is:,,,, 1,, 1 (3) An equation to apply a rotation operation to the element, of the motif at the rotated point, on the canvas is:,,,, 1,, 1 (4) An equation to apply a rotation operation to the element, of the motif at a rotated point, on the canvas is:,,,, 1,, 1 (5) An equation to apply a flipping operation to the element, of the motif at a flipped point, on the canvas is:,,,, 1,, 1 (6) An equation to apply a flipping operation to the element, of the motif at a flipped point, on the canvas is:,,,, 1,, 1 (7) An equation to apply a flipping operation to the element, of the motif at a flipped point, on the canvas is:,,,, 1,, 1 (8)

An equation to apply a flipping operation to the element, of the motif at a flipped point, on the canvas is:,,,, 1,, 1 (9) 3.3 Pattern Exporting The pattern exporting means an ability to export a selected motif s segment on the canvas to a destination file. We provide three types of exporting file: a motif file, a tie-up file and a standard weave information file (WIF). To export a selected segment as a motif file, the segment s size and its binary data have to be stored to the file. This file could be reused as an import motif and is used as a component for design another motif, and the data from import file would be read and assigned to be current values of canvas s elements (see equation (1) for mathematics term). For a tie-up and WIF file are used in other modules of our work, in this publication we are not focus on them. 4. Using the LT-TieUp Module To show how the LT-TieUp module generates a pattern, we prepare an example to create a pattern from a fig.3 which is a pattern diamond of Naga head and flowers. In religiously meaning, this pattern exhibits a group of nagas. Lao people often used textile decorated this pattern to cover their treasures or their valuable assets, because they believe these nagas would protect their possessions. The generation process would be explained step by step start from making a list of demanded motifs. We need to find how many build-in atomic icons to be used in this design, and how many new icons or motifs we have to create. We found that the pattern is symmetry and its structure is composited by eight lines of atomic icons and one specific diamond motif in the middle of the pattern, so its unique pattern is a quarter part of the pattern. It means that to generate this pattern we need to design only one over four area of it. We supposed that the eight line components are able to create from build-in icons only a diamond in the middle of the pattern is a new created motif. A fig. 4 shows the graphical feature of the new diamond after created. A fig. 5 to fig. 7 show graphical features of the rest components, they expose unique icons at lower part and line of icons at upper part. Fig. 3. A Photo of pattern: diamond of Naga head and flowers.

5.(a). 5.(b). 5.(c). 5.(d). Fig. 4. A new created diamond motif (Size 33 x 38) Fig. 5. Lines of atomic icons are used in design: lower part shows unique icons and upper part shows their lines. 6.(a). 6.(b). 7.(a). 7.(b). Fig. 6: 6.(a). a line of Naga head (icon s size:16 x 47). 6.(b). a line of diamond Jik flower (icon s size: 10 x 40). Fig. 7: 7.(a). a line of diamond blend flower (icon s size: 14 x 53). 7.(b). a line of diamond star flower (icon s size: 14 x 48) We start the process from adding the created diamond in fig. 4 into empty area of the canvas, because we would like to design from inner to outer of the pattern. After that, we create and add icon s lines from fig. 6 in an order: fig.6.(b), fig.6.(a) respectively, the result shows in fig.8. If we look back on fig. 3 again, the line of Naga head is a component to determine a height of the pattern and the end of the line needs a little edit, thus fig. 9 shows motif s result after adjusted the line of Naga head. We could see that the patterns are generated in diagonal direction.

Fig. 8. Motif s result after adding line of Naga head Fig. 9. Motif s result after adjusted line of Naga head We keep adding the lines follow from an order: fig.5.(b), fig.5.(a), fig.5.(c), fig.7.(a) respectively, the corresponded result illustrates in fig. 10. At this point, we reach to a component that defines a width of our desired pattern and we could precisely know a size of our pattern. The result in fig.10 shows an empty area that need more adding elements in order to get a final result the same as the example pattern. We continuous add lines of icons from an order: fig.5.(c), fig.5.(a), fig.5.(b), fig.7.(b), fig.5.(b), fig.5.(a), fig.(c) and finally fig.5.(a). Remark: in this last process we keep the start point and end point in a boundary of the pattern. A pattern on fig. 11 exposes the final result of unique pattern of a given pattern. Fig. 10. Final size of motif for pattern generation (size: 102 x 173) Fig. 11. Motif result after filled regarded lines into an empty space To get a similar pattern as the given pattern we need two more steps, firstly we apply an operation to copy our last output and then flip it in vertical direction, so a first half of the desired pattern is produced (the result shows in fig. 12). The final step, we copy the output from fig.12 and then flip it in horizontal direction, so the second half of the pattern is produced

(the result shows in fig. 13). Finally, we get our purposed pattern which could be exported any file as explained in section 3.3. Fig. 12. A result of a first half Pattern after applied copy and vertical flip operation to the unique pattern Fig. 13. Copy and horizontal flip first half pattern to get second half pattern (size 203 x 245) 5. Conclusion The LT-TieUp module proposed in this paper encourages the motif design task for any style of textile patterns, particularly the motifs of Lao traditional textiles. The implemented mathematical and computational methods in the module enable the design process to be flexible and efficient. The built-in objects in the module are constructed from benchmarks taken from original Lao textile patterns. These built-in objects are a tool to facilitate designers to easily generate Lao traditional motifs. The binary matrix is another key in this paper, it is

used to present a structure of the motifs, we declared the canvas and motifs as binary matrices where motif s operations on the canvas are created regarding to the criteria of the weaving patterns. For, our further work we will keep investigating to improve facilities in the LT-TieUp module and we are considering on a computing technique to provide temporary memory space for storing new created motifs at design time and they could be able to reuse during design. References [1] Ellison Banks Findly. A Protective Spirit in Lao-Tai Textiles: The PII Nyak and Its Indian Antecedents In the Journal of Lao studies, Volume 2, Issue 2, pps 47-66. ISSN: 2159-2152, November, 2011. [2] Dara Kanlaya, Khongthong Nanthavongdouangsy Saisanith, Vienkham Nanthavongdouansy, Chanthasone Inthavong, Douangdeuane Bounyavong, Kiyoko Yasui. Legends in the Weaving, ISBN: 974-548-202-1, 2001. [3] Tagwerker, Edeltraud. Siho and Naga- Lao Textiles. Frankfurt am Main, Berlin, Bern, Bruxelles, New York, Oxford, Wein, 2009. 195 pp., 33 coloured fig. ISBN 978-3-631-58689-1. ISBN 978-3-653-01871-4 (ebook). [4] Mathematics for symmetry in Frieze group online http://en.wikipedia.org/wiki/frieze_group [5] Mathematics for symmetry in Wall paper group online http://en.wikipedia.org/wiki/wallpaper_group [6] Mary F. Connors. Lao Textiles and Traditions. Oxford University Press, 1996. Original from University of Michigan. Digitized in 19 th December, 2007. ISBN 9835600015, 9789835600012. 82 pages. [7] Nathaniel A. Baylas IV, Teofina A.Rapanut. Weaving Symmetry of the Philippine Northern Kankana-ey. Bridges 2012: Mathematics, Music, Art, Architecture, Culture. [8] Vytautas MILASIUS, Jurgis KATUNSKIS, Dalia TAYLOR. New Ornament Notation for Woven Fabrics ISSN 1392-1320 MATERIALS SCIENCE. Vol. 13, No. 2. 2007. [9] M.A Hann and B.G. Thomas. Beyond the Bilaterial-Symmetry in two Dimensional Design. IASDR07, International Association of Societies of Design Research the Hongkong Polytech University 12 th to 15 th November 2007. [10] Vytautas Milasius, Dalia Neverauskiene, Jurgis Katunskis and Ilona Kazlauskiene. The Mathematical Basis of Ornamentation of Patterned Woven Fabrics. FIBERS & TEXTILES in Eastern Europe October/December 2002. [11] Lila Lekka and Sofia Dascalopoulos. Motifs and Symmetry Characteristics of the Ornamentation on Traditional Greek Woven Textiles from the Area of the Aegean. FIBERS & TEXTILES in Eastern Europe July/September 2008, Vol. 16, No. 3 (68). [12] Ingrida Zdanaviciute, Vytautas Milasius and Jurgis Katunskis. The Peculiarities of the Ornamentation of Lithuanian Traditional Woven Textiles. FIBRES & TEXTILES in Eastern Europe April/June 2006, Vol. 14, No. 2 (56)