Application of Reflective Symmetry on Coptic Tapestries towards Developing Equilateral Kaleidoscopic Textiles. M. Asim Naeem Email: asimnaeem.pifd@gmail.com asimnaeem@pifd.edu.pk Pakistan Institute of Fashion and Design, Lahore, Pakistan. Associate Professor, Fashion Design Department Abstract With the active life style, new developed technologies and fast changing trends, pressure is build up on practicing designers to come up with new designs to meet with the increasing demand. Antiquity always provides an effective source of inspiration. Some ancient pieces of textiles only survived in Egypt due to dry climate, provides detailed information not only about their construction techniques but also their colours, designs and surface treatments which explains cultures, invaders, influences and religious practices. The focus is how to explore these ancient pieces of textiles and develop a range of infinite prints by unfolding the mystery of first, second and third reflective virtual images? The outcomes incorporating latest technology have diverse applications. Too soon is as dangerous as too late. The designer must sense the timing of upcoming fashion trend. The next step is often to consult the textiles of earlier days, looking for something that can be modified for the arriving moment- something old that can be recast as new. How original is intensely mixed up with the aged that an appropriate treatment through technology the aged turns in to original? Keyword: Coptic textiles/ Antique source, Polarization of light, Old into New Introduction With the increase in demand of designs by consumers, fashion and textile designers always look for different possibilities of creating new designs and textiles. It is a standard procedure to look at existing crafts or imagery for ideas and mix it with the inhand technology. Ancient cultures and civilizations, where things were discovered and invented with quality and technical originality are an undeniable source of inspiration for today’s designers. Egypt being a great trading center for textiles with a rich history of textile crafting techniques has been a major source of inspiration for designers throughout the last century. Some ancient pieces of Coptic textiles that only survived in Egypt due to its dry climate, provide detailed information not only about their construction techniques but also their colors, designs and surface treatments which explains cultures, invaders, influences and religious practices. The artistic appeal of Egyptian Coptic textiles might be due to their antique appearance. Their popular naïve style is as un-classical as could be and has an eclectic charm of craft objects, the attraction of which does not fluctuate with changes in fashion. The process is to manipulate a triangular selected section from the imagery of these ancient pieces of textiles and develop a range of infinite prints with the similar feel, by unfolding the mystery of kaleidoscopic first, second and third reflective virtual images. The outcomes incorporating latest technology will have diverse applications. History A historical study of textiles requires knowledge of people who designed, wove and used them. Coptic textiles were woven by native Egyptians known as Copts, who lived in Northern Egypt in the beginning of Christian era until Rome fell, and until the Caliphs of Islam conquered Egypt. The Coptic period (late 3rd Century A.D. to mid-7th Century A.D) is Egyptian era sandwiched between the times of Pharos and the Muslims. [1, 3, 4, 5] With the advent of colonization several invaders and conquerors entered Egypt, creating a cultural infusion that transformed its native arts and crafts. At the time of the late antique world (4th to 7th Century A.D) when the ruling body was Egyptian Pharos the art of ancient Egypt was brewed together with Classical (3rd to 4th Century A.D), and later with Christian art (5th to mid-7th century A.D) and Muslim influence (mid-7th to 12th century A.D). Tapestries created are evidence to that change in style. [1] (Insert Figure 1 here) Fig 1: Fragment of a Tunic, Egypt. 9th century, Wool, Tapestry and Tabby Weave, 53.5 X 70.5 cm [1]
It is hard to look at Egyptian history and textiles, without some echo of triangular pyramid coming to mind for the reason that the pyramids are second eminent after the Pharos. Its connection with the pyramid shape suggests immortality and eternity. Symbolic shapes have different meanings that in turn also evolve through the passage of time. Things which at one point were powerful for one ethnicity become ornamental for another. What is ornamental at one point in time might have once been a symbol of power. This transformation of symbols is witnessed in their popularization through the professions of design when they appear infinitely on our everyday clothes, dresses for our children, bed covers, floor coverings and carpets, wall hangings, decoration on pieces of furniture, curtains etc. [2] The innumerable images that wrap our bodies and decorate our homes are in fact seen so often that they demand special attention to be seen at all. Each design is not only the pregnant parent of some future design but also a descendent of a design in the past. It is the nature of textile pattern to duplicate itself endlessly so that the basic image is lost in a sea of repeats [2]. Similarly multiple mirror symmetry of a triangle can produce unpredictable, infinite kaleidoscope patterns. In this instance the designer’s urge might be to make the unusual and the yet unseen. Similar to the processes of infinite repetition in textile pattern making, a kaleidoscope functions on the principle of “Multiple reflections or Reflective symmetry” where numerous mirrors are placed at a different angle to reconstruct an illusionistic image. Usually there are three mirrors placed at 60° to form an equilateral triangle. The basic mathematical rule in the construction of a kaleidoscope is the angles on which the mirrors are placed. These must be at even divisions of 360° of a circle. The incorrect placement or overlap of the mirrors would disturb the infinity of symmetric design. [6] Kaleidoscopic designs have been made in the textile design industry as per recent trends, by using 60°- 60°- 60° equilateral triangle phenomena of kaleidoscope with the basic aim of how the original is intensely mixed up with the ancient craft. Through this process an appropriate application of technology to an ancient artefact turns it in to a new original image. To me as a designer this process is interesting because through very slight variations in the size or placement of a triangular section of an ancient pattern renders a completely new symmetrical design. Although all the designs look different they are produced from the same source. This infinity of possibilities is what fascinates me. Process To understand the kaleidoscope multiple reflections one has to understand the principle of mirror reflection. Rays of light bounces back from the mirror as the ball bounces off from a hard surface. In physics it is Angle of incidence = Angle of reflection. In easier words, light rays will reflect back in the same degree angle as the degree they fall on the mirror; reflections are formed at the back of the mirror where the reflected light rays will intersect. [6] This section focuses on elaborating the process I specifically employ in obtaining the patterns through the application of reflective symmetry to Coptic textile patterns. I begin by selecting an equilateral triangular section from one of the original Coptic textile images (Fig No: 2a), while assuming that all three sides of the selected triangle are front-surface mirrors. For a better understanding and to reduce the complication by providing reference points, three orientation dots – one small, one big and one hollow - are superimposed on the selected section (Fig No: 2b). These three dots provide ample information to decide the placement of reflective images. Every dot is studied separately starting with the solid small dot. Then I make an assumption that two light rays emerging from the dot are falling on the base mirror at a certain degree and bouncing back at the same degree indicated by the arrows. Since the reflections are not real, they are virtual; this means that the light rays do not intersect in reality. The image reflection is located by extending the reflected light rays. Dotted lines are used to indicate that the rays are in fact virtual. A reflection of an object is located where these two virtual light rays intersect. The dot underneath the mirror shows the position of a virtual image (Fig No: 2c). The same principle of locating the reflected image trough reflected light rays is used to locate the position of the solid big and hollow dots respectively (Fig No: 2d & 2e). The resulting reflective image of all three dots is in the flipped bottom triangle (Fig No: 2f). The same principle of locating the reflected image trough reflected light rays is used to locate the position of dots in the Right and Left mirrors (Fig No: 2g). The resulting images are gathered to provide the point of reference for the first reflected images of the kaleidoscope. The actual image is the middle triangle with the reflected images in the adjoining triangles (Fig No: 2h). The selected image is manipulated in the same way along with the orientation dots (Fig No: 2i). Then, the orientation dots are removed to reveal the result of the first reflected images (Fig No: 2j). (Insert Figure 2 here) Fig 2: First Reflection Placement Study
The resulting image of the first reflection placement study is called “Common Reflections�, reflected in a single mirror. It is due to the presence of an additional mirror the infinity of reflected images is created, which is the characteristic feature of a kaleidoscope. There are two rays of light that emerges from the small dot and travel in the direction of the base mirror. The light rays reflect from the mirror surface but the path of light does not stop with a single reflection. After reflecting from the base mirror, the light rays fall on the right mirror and bounce back. This second reflection also produces a second virtual image. The light rays are reflecting back in the same angel as they are falling on the mirror on the right side. These angles are extended in dotted lines till they intersect to locate the position of second virtual image of small dot at the back the mirror (Fig No: 3a). Limiting to the principle of light path, which is starting from a dot then traveling towards the base mirror in a certain angle, reflecting from the base mirror in the same angel in the opposite direction traveling towards the right mirror, again reflecting from the same mirror in the same angle as they are falling. These second reflecting light ray angles are extended in dotted lines to locate the position of the virtual image for the big and hollow dots (Fig No: 3b & 3c). The resulting virtual image is on the right hand side (Fig No: 3d). The next step is to obtain a virtual image from base to the left mirror. As per the above study from the base to the right mirror, starting with the small dot the same path of light reflections was applied, the image is positioning itself on the left hand side (Fig No: 3e). Similarly the big and hollow dot virtual second reflection image will also fall on the left side (Fig No: 3f & 3g). The resulting diagram of virtual images obtained from base to right and left side reflection is, original image in the middle with thick outline and the virtual in the same direction triangle on right and left hand side with thin outline (Fig No: 3h). The same procedure is applied twice for left and right mirrors to get the full scheme of second reflective kaleidoscopic images. The resulting image is where the original dots are marked in Black, first set of reflections (common reflections) and second reflective virtual images produced by all three mirrors in Grey (Fig No: 4a). The selected image is manipulated in the same way along with the orientation dots (Fig No: 4b). Orientation dots are removed to reveal the result of the first and second reflected virtual kaleidoscopic images (Fig No: 4c). (Insert Figure 3 and 4 here) Fig 3: Second Reflection Placement study. Fig 4: Results of Second Reflection Placement Study
Next is the study of third reflective virtual images to complete a hexagon pattern under the terminology of equilateral kaleidoscope, where six equilateral triangles will complete the requirement of 360 degrees of a circle. As per the first and second reflection placement study we begin with the small dot again.
Two rays of light emerges from the small dot and travel in the direction of base mirror. As explained earlier, the light rays reflect from the mirror surface but the path of light does not stop with a sole reflection. After reflecting from the base mirror, the light rays travel upwards to the right mirror and bounce back. Now both the rays are moving in the direction of the left mirror and reflect again for the third time. This third reflection is producing a third virtual image. The light rays are reflecting back in the same angel as they are falling on the left mirror. These angles are extended in dotted lines till they intersect to locate the position of the third virtual image of small dot (Fig No: 5a). Following the same principle of the light path, which is starting from a dot then traveling towards the base mirror in a certain angle, reflecting from base mirror in the same angel in the opposite direction traveling towards the right mirror, again reflecting from the right mirror in the same angle as they are falling, then reflecting from the left mirror for the third time. These third reflecting light ray angles are extended in dotted lines to locate the position of virtual image for the big and hollow dots (Fig No: 5b & 5c). Third reflective images produced by the base mirror till this point are marked in Grey color, whereas the original dots are still Black (Fig No: 5d). Next is to obtain third virtual images from base to the left mirror. As per study from the base to the right mirror, again we begin with the small dot followed by the big and hollow dots. Applying the same path of light reflections, the image is positioning itself on the right hand side (Fig No: 5e, 5f & 5g). The virtual image obtained from the base to the left and then the right sides third reflection is marked with Grey color whereas original dots are in Black (Fig No: 6a). Another third reflective virtual image is obtained from another light path. Assume that the two light rays emerge from the small dot and travel towards the right hand side corner of the base mirror. As explained earlier, the light rays reflect from the mirror surface but the path of light does not stop with a sole reflection. After reflecting from the base mirror, the light rays travel upwards to the right mirror and bounce back. The angle of second reflection is such that now both the rays are again in the direction of the base mirror and the third reflection will happen in the base mirror. This third reflection is producing a third virtual image. The light rays are reflecting back in the same angel as they are falling on the base mirror. These angles are extended in dotted lines till they intersect to locate the position of third virtual image of small, Big and hollow dots (Fig No: 6b, 6c & 6d). The third virtual reflection obtained from the base to the right and then the base mirror is marked in Grey color whereas original dots in Black (Fig No: 6e). The same procedure is applied twice for the left and right mirrors, to get the full scheme of third reflective kaleidoscopic images. The resulting scheme is where the original dots are marked in Black, first set of reflections (common reflections), second and third reflective virtual images produced by all three mirrors in Grey (Fig No: 7a). Selected triangular section is manipulated in the same way along with the orientation dots (Fig No: 7b), later orientation dots are removed to reveal the result of first, second and third reflected virtual kaleidoscopic images (Fig No: 8). (Insert Figure 5, 6, 7 and 8 here) Fig 5: Third Reflection Placement Study. Fig 6: Cont. Third Reflection Placement Study. Fig 7 Results of First, Second and Third Virtual Reflections. Fig 8: Final Outcome of Selected Triangular Section with First, Second and Third Reflected Virtual Kaleidoscopic Images.
The final kaleidoscopic image has original equilateral triangle image, three common reflection images, six second reflective virtual images and nine third reflective virtual images. This entire scheme completes the requirement of infinite equilateral kaleidoscopic pattern construction. There is no identification of a motif in the initial selected triangular portion but after the final formation an abstract appearance of Floral, Geometrics and Ethnics can be seen. Colors are as per inspirational image. Patterns can be scaled up or down for product, apparel and home furnishing. Depending on the size and shape of product, sections and motives can be selected from within the final formed infinite kaleidoscope design. Several running prints and borders can be obtained for apparel. Diverse range of combinations for interior and home furnishing can be produced from single source image. All these designs are constructed digitally they can be produced through Digital Printing, running designs with flat color on Rotary Printing, more simplified on Silkscreen Printing, compositional designs with engineered placements of motives and borders with limited colors with Flat-bed Printing and to get the real feel of tapestry different gauge yarns can be introduced in Jacquard weaving or knitting. As a teacher and practitioner I have experienced and believed, while designing the quick and favorable, unpredictable original results can be achieved by mixing arts, crafts, physics and mathematics. Small little things and crafts from surroundings with an appropriate twist through in-hand technology establish amazing design trends. Science always plays an important role in the background of art and design field, one has to be more observant and explore with modern and practical approach. Bibliography 1. Rutschowscaya, Marie-HÊlèn. Coptic Fabrics (United states of America: Adam Biro, 1990). 2. Meller, Susan & Elffers, Joost. Textile Designs (United kingdom: Thames & Hudson Ltd., 1991). 3. sustainability, Institute of Biodiversity Sciences &. Coptic Textiles. 1998. http://researcharchive.calacademy.org/research/anthropology/coptic/index.html (accessed September 21, 2016). 4. Hoskins, Nancy Arthur. Coptic Textiles. 2006. http://fashion-history.lovetoknow.com/fabrics-fibers/coptic-textiles (accessed September 21, 2016). 5. Krueger, Adriana Calinescu & Nancy. Coptic Textiles from Ancient Egypt. 1999. http://www.indiana.edu/~iuam/online_modules/coptic/cophome.html (accessed September 21, 2016). 6. Wong See Wan, Wee Sean Han Adrain & Yang Xiaotian Grace. Kaleidoscopes: Reflections of Mathamatics & Art. http://www.math.nus.edu.sg/aslaksen/gem-projects/maa/Kaleidoscopes/kscopes.html (accessed September 21, 2016).