GEM1518K: MATHEMATICS IN ART & ARCHITECTURE

GROUP #7: ALL ABOUT BATIK!

MEMBERS:

Fazylah Bte Abdul Rahman – U020631J Liu Ping An, Tabitha – U010484E

Nur Azlinawaty Abdul Rahman – U021567M Nurhidayah Bte Mohamed Ali – U020446R

Raudha Bte Rahmat – U020445E

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Table of Contents

1. Introduction 2. Preparation of Batik 3. The Process of Batik Painting 4. Mandala 5. Mandala Symmetry 6. Mandala Designs 7. Geometric Designs 8. Islamic Influence 9. Islamic Influence in Symmetry 10. Free Forms 11. Frieze Patterns 12. Frieze Patterns in Different Applications 13. Rosette Patterns 14. More Rosette Patterns 15. Wallpaper Types 16. Wallpaper Patterns in Maths 17. Wallpaper in … 18. Conclusion 19. Modern Batik 20. Acknowledgements 21. The Cloth

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Geometry in Art and Architecture is always around

us but unless we take a closer look and be more sensitive

to the patterns around us, these beautiful designs will

just bypass us day after day.

Batik designs are becoming popular with the masses

as there seems to be a trend towards ethnic and

traditional clothes nowadays. What was perceived to be an

out of fashion apparel is now given a new twist to suit the

modern times. For example, in the book written by Iwan

Tirta, he mentions that ‘traditional ceremonial clothes

and court costumes share several characteristics with

today’s high-fashion wear’. Pleasing to the eye, both in

terms of pattern and colours, batik is a form of art that

gives free rein to creativity.

On closer inspection, batik designs incorporate many

concepts of symmetry. In this project, we examine the

various batik patterns and show how they display

concepts like reflectional, rotational symmetry. Upon

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understanding the concepts we then attempt to classify

the various batik patterns into the 3 symmetry patterns

namely, rosette, frieze and wallpaper.

We also observe the Islamic influence on symmetric

patterns. Incorporating the concept of mandala symmetry

we then try to explain the mandala symmetry present in

the designs. A brief history of batik and the process to

making batik is also included in this project.

Lastly, a batik piece made by us is presented to

illustrate the concepts we have understood and

observed. The batik design is divided into 3 designs of

which it incorporates ideas of mandala symmetry and the

different symmetry patterns.

While batik has been found all over the world from

China to Germany and even Egypt, it reached its highest

accomplishments in Java.

Batik is most prevalent on the Indonesian island of

Java. Some scholars believe that it was an art form that

belonged only to the privileged and royalty. Certain

patterns were worn only by the members of the royal

family. Other scholars, however, believe that it was also

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used by the common people. In fact, one of a young lady’s

accomplishments would be to be able to handle a canting

(the pen-like instrument used to apply the wax to the

cloth) with some skill.

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Preparation of Batik The Cloth Batik is made of natural materials and fabrics like

cotton or silk are generally used. These cloths can

absorb the wax used in the dye-resisting process. The

cloth that is being used is washed and boiled in water

many times before the application of wax, to rid it of all

traces of sizing materials. In the past, the cloth would be

pounded to make it smooth and supple to take in the wax

design.

The Canting A small, thin-walled spouted copper container

called a canting that was connected to a bamboo handle

would then be filled with wax. The artisan would then use

the canting and draw the design on the cloth.

The Cap Nowadays, to enable a higher volume of production of

batik, the cap is used. The cap is a copper block that makes

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up a design unit and saves time when designing multiple

pieces of the same pattern.

The Wax Common waxes used for batik consist of a mixture of

beeswax and paraffin. There are different grades of wax

and generally, cheaper waxes are used to cover the

bigger areas. The wax must be kept at a proper

temperature. Wax that is too cold will clog the spout of

the canting but wax that is too hot will flow too quickly

and be uncontrollable.

The Dyes Traditional dyes were made from natural

ingredients and were mainly beige, blue, brown and black.

Dyes were made from leaves of plants, molasses sugar

and lime and tree sap used as a fixing agent.

The Process of Batik Printing 1) The design is first drawn onto the cloth

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2) Wax is applied to the areas of the cloth that the

artisan wants to remain the original colour of the

cloth.

3) The wax is allowed to cool and harden.

4) The waxed fabric is immersed in the dye bath of the

first colour. The longer the cloth is left in the bath,

the darker the hue of the colour.

5) Wax is reapplied over areas that the artisan wishes to

remain the colour of the first dye or another colour at

a later stage in the dyeing process. Where an area that

has previously been covered with wax needs to be

exposed and dyed, a small knife is used to scrape away

the wax.

6) Steps 3 to 5 are repeated for the different required

colours.

7) If a marble effect is desired, the wax is intentionally

cracked and before being placed in a dye bath. The dye

seeps into the tiny cracks that create the fine lines

that are characteristic of batik.

8) Finally, all the wax is removed by heating the cloth in

hot water and sponging the wax off.

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Needless to say, the number of colours in batik

represents how many times it was immersed in the dye

bath and how many times wax had to be applied and

removed. A multi-coloured batik represents a lot more

work that a single or two-colour piece.

MANDALA The Sanskrit word “Mandala” means ‘circle’. The

mandala is used to symbolize wholeness and its pattern

can be found in science, religion, art and architecture.

Mandala can be observed in nature. Whether in cells,

ice, rocks, spider webs, flowers or the rings found in tree

trunks, the primal mandala pattern can be found. Within

the Milky Way, galaxy is our solar system, within which is

earth. Each is a mandala that is part of a bigger mandala.

The “circle with a centre” pattern, we see, is the basic

pattern in nature from micro to macro.

Mandala can be found in many religious patterns and

art forms. In Asia, the Taoist “yin-yang” symbol

represents opposition as well as interdependence. The

Indians create sand mandalas to demonstrate the

impermanence of life. Mandala patterns are common in

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batik prints too. Further from us, we have symbols like the

‘star of David’ and circular Aztec calendars that were

both religious expressions and time-keeping devices.

Mandala can also be observed in architecture. These

can be seen in Buddhist stupas, Muslim mosques and

Christian cathedrals where the principle of a structure

built around a centre is a common theme. Another famous

structure would be Buckminster Fuller’s geodesic dome

structures which show the mandala.

The mandala can be used to explore art, science,

religion and life itself. Carl Jung said that it symbolizes

“a safe refuge of inner reconciliation and wholeness” and

is “a synthesis of distinctive elements in a unified

scheme representing the basic nature of existence”.

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Mandala patterns in general sense of the word:

religion and culturally motivated.

Pictures courtesy of: http://www.mandalaart.com/mandalas/mandalas1.html Mandala in the Buddhist perspective:

Colour Element Means of Transport

Centre: Vairocana White Ether Lion West: Amitabha Red Fire Peacock East: Aksobhya Blue Water Elephant

South: Ratnasambhava Yellow Earth Horse North: Amoghasiddhi Green Air Mythical Bird

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Seemingly looks like a compass of sorts however

this figure represents the beliefs of the Buddhist.

Centre represents the symbol of Buddha in which 8

Buddhas of meditation surround the centre. These

figures, facing the corners of the earth form together a

lotus flower.

Mandala symmetry is portrayed in such designs,

which are also represented in batik as seen in the

following section.

What Is Mandala Symmetry?

Graphic symbolic pattern usually in the form of a circle

Connection with maths : mandala symmetry makes use of radial symmetry and hence in so doing , reflects the different aspect of symmetry like balance, reflection, rotation and translation

General mandala symmetric pattern : round shaped images consisting of repeated symmetrical radiating from the centre

Mandala eminent form of art in many different cultures

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Central motif radiates out to provide balance where the elements in a composition are regularly arranged and

radiates from the central point.

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Geometric Designs Non-Geometric Designs(Semen)

Mandala

Mandala Influence: Central focus

Characteristics: • leaves or buds • animals on

background of leaves

• animal and leaves combined with the wings of the mystical garuda eagle

Tumurun Sri Narendo is a font of symbolism. It is made up of the coat-of-arms around a symbol of the world globe (idea of mandala), a nest of cotton and rice plants that signify prosperity and the diagonals in the background that represent the rays of the sun.

West Java: Kain Simbut made up of simbut figures, geometric forms like scrolls, swastikas & triangles

Hand drawn batik on silk organza adorned with prada

Kembang Kenikir has resemblance to the cosmos, with sun-yellow petals that radiate outwards from the centre (idea of mandala), ‘from which all graces flow’.

Central Java: Jlamprang motif consists of intricate borders & edgings. (The Patula)

Gringsing pattern is one of the oldest batik motifs. Period: 19th century AD, Kingdom of Kediri, East Java. Gringsing motif is used as the background. - Dutch scholar Rhouffaer

The legendary event of the sacred geese of India being confused with the origin story of Jambi city has the design of four pairs of geese arranged around a focal point.

Ceplok: Made up of lines that form squares, circles, slanting rows or other forms that are arranged in a square composition.(square patterns; ancient temple reliefs in central Java) Line of symmetry: 90º

Gajah birawa, awesome elephant, belongs to the semen family of designs.

Parang patterns, ordinary diagonal geometric patterns (line of symmetry 180º) distinguished by rows of lozenges or diamond shaped patterns (mlinjum) after the fruit of the so tree

The cirebon, antique dodot or kampuh and stormy cloud design, belong to the diagonal geometric motifs category.

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With the coming of Islam, even the batik designs were

strongly influenced by the Islamic faith. In some designs,

there is a tinge of Middle-Eastern influence such as the

Turkish designs. The latter discouraged the depiction of

living creatures; hence batik designs are normally made

up of floral and geometric patterns.

Batik cloths were also decorated with calligraphy

written in Arabic. For instance, in Sumatra, men wore head

cloths that have Islamic phrases written in Arabic,

printed onto the batik cloths.

Most often, the Arabic phrases are ‘Bismillah’ – a

phrase used at the start of each surahs of Al-Quran and

also expressed before any major undertaking – or the

‘Shahada’ - the Muslim profession of faith.

Batik cloths were also made into selendangs or a

woman’s head cloth. Good quality selendangs are

normally worn by aristocratic Muslim ladies. The

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selendangs worn by these women are usually large and

rectangular, in order to cover both their heads and

shoulders.

However, different styles were also produced for

customers from other ethnicity and/or religious beliefs.

An interesting aspect of this in relation to Maths in art

would be the illusion that such an Islamic-influenced

batik creates. At one glance, one may perceive that such

batik designs are symmetrical. However, upon closer

observation, no symmetry is found as the calligraphy

‘disrupts’ what would otherwise be perfect symmetry.

These examples are illustrated below.

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A transgression of the parang rusak. Here this pattern is

akin to those used by the royals. Lines seem to be continuous in nature however bearing no form of

symmetry as a whole pattern.

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This seems more like a piece of artwork. There are elements of nature involved – the leaves, vines and flowers form a big part of the batik design and thus,

emphasizing on nature. The bird livens up the pattern too.

DeWeSioffi

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Borders: No symmetry Angle of

Rotation: 180� Type: pmg

scription: st Java: Kain

mbut made up simbut gures

One-sized lozenges diagonally aligned.

Absence of vertical reflection

Absence of glide reflection

Absence of half turns

Type: p111

Description: Parang

Smaller and larger lozenges diagonally aligned.

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Frieze Patterns in Different Applications

In Ropes

Repeated

translational patterns as

shown below.

Frieze Patterns in Iron Rod

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Has 1-fold rotational symmetry.

Has reflection symmetry (1-fold

f

Has 2-fold rotational symmetry. Has 2-fold reflectional symmetry.

Hence, it is type D2.

Description: The famous mega-mendung, or stormy clouds pattern from Cirebon. The motif made use of 8 shades of blue instead of the usual 4. This results in an

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outstanding piece, deviating from the original pattern in which the clouds are arranged along diagonal lines.

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More Rosette Patterns … Ormaig rock carvings

Rosette

Rosette Rock Sheet

Rosette in Guitar

Carvings which signify the craftsman’s skill

Photo of Carved Rosette on

Title Bowl with a Rosette Pattern Period 5th - 4th centuries B.C.

Materials Silver Dimensions H-6 D-33

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No angle of reflection

180� rotation symmetry

Horizontal or

Angle of Rotation: 90� Presence of reflection

Presence of reflections in lines

which intersect at 45� Symmetry Type: p4m

Description: There are many ways of looking

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Technological terms…

Wallpaper to liven up one’s computer screen

Housing…

Wallpaper for window Magic blue Raspberry natural

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Jay and wolf

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As one can see, batik has evolved in many ways, along

the many decades. What was previously an Indonesian

culture and heritage has now assimilated itself into our

multi-cultural society and in Southeast Asia. Both local

and foreign fashion designers have adopted the unique

batik patterns into their creations, enhancing the

original motifs into creative modern designs. There have

also been adaptations of the batik into something more

trendy and casual wear, with a touch of artistic

ingenuity.

The batik, as we have seen, possesses interesting

Mathematical and artistic perspectives. One can see how

different types of patterns display the various forms of

symmetry, mainly the rotational and reflectional

symmetries, and the nifty method the batik designers

employ cultural or religious ideologies into the batik.

There are different batik patterns which the batik

painters use to create their cloths such as the frieze

and rosette patterns. It is amazing how a simple pattern,

such as a triangle or a circle, once merged with own or

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other shapes and given different colours could appear

as beautiful and captivating as the batik designs we have

seen earlier.

Batik will continue to be a predominant trend in the

Southeast Asian region, concurrently spreading its feel

to the European and American countries. Many foreigners

are intrigued with the batik and its numerous motifs.

There are a number of sites created by them to broaden

one’s knowledge and to discuss about batik as well as the

religious ideologies; for instance the mandala. Batik was

and still is about clothing. It will be a part of all

Southeast Asians for many times to come, and hopefully

spreading its wings to the four corners of the world.

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Acknowledgements • [2002] Teachworth, Ron. What a Mandala is.

http://www.ronteachworth.com/mandAbt.html

• What is a Mandala? Mandala Project. http://www.mandalaproject.org/What/Main.html

• [1999] History of Batik. The Batik Guild. http://www.batikguild.org.uk/history.htm

• [2001] Story-of-Batik.com - History of Batik page. W3Commerece Inc.

http://www.story-of-batik.com/html/history_of_batik.html

• [1998] Indonesian Batik Information. Information Music Shop. http://www.indonesianmusic.com/batik.htm

• [2002] indotips.net. worldtips.net

http://www.indotips.net/english/culture/culture_batik04.html • MandalaArt.com - Mandala Art. Mandala Art.

http://www.mandalaart.com/mandalas/mandalas1.html • [2003] Hansen, Jytte. Mandala. http://www.jyh.dk/indengl.htm • [2002] Séquin, Carlo H. CS285 SP2002 Lecture Page.

http://www.cs.berkeley.edu/~sequin/CS285/LECT/L5.htm • Free Chip Carving Patterns from Chipping Away. Chipping Away.

http://www.chippingaway.com/Patterns.htm • Trevor Semple Guitars. Trevor Semple Guitars.

http://www.sempleguitars.com/making/tsrosette.htm • [2001] Itie van Hout (ed). Batik Drawn In Wax. Royal Tropical Institute/KIT

Publishers – Amsterdam. • [1999] J. Achjadi. Batik ~ Spirit of Indonesia. Yayasan Batik Indonesia, Jawa Barat.

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Our own piece of cloth is made up of three parts.

The Mandala Rosette Pattern

Our mandala rosette pattern is one of a flower

(kembang) with its petals stretching out to the edges. In

line with the Indic concepts of space and authority, the

pattern is concentrated at the centre and getting less

and less dense as we move out. This pattern represents

the Indic world view, which sees everything as structured

around the notion of a galaxy, with the all-important sun

as the centre of the universe and the increasingly

insignificant stars drifting out towards the edges.

Since another way of referring to the

cosmologically ‘dense’ centre is as the ‘exemplary’

centre, the ideal mandala pattern would have either a

circular or diamond-shaped centre which is white in

colour as white represents peace, serenity and calm. The

centre should ideally have no patterns within it, as the

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exemplary core should be clear-thinking and

uncluttered by ordinary worldly temptations.

The mandala ideology is most strongly seen in the

popular deva-raja cult in maritime Southeast Asia as a

local adaptation of the Hindu based belief.

Our particular mandala pattern (theoretically) has

both 90o rotational symmetry, with the exemplary centre

as the centre of rotation. It would have 4-fold

reflectional symmetry as well if not for the decorative

white lines around the actual kembang pattern.

The Parang Rusak

The second pattern in our cloth is the traditional

Parang Rusak pattern. The Parang Rusak is a traditional

‘forbidden’ pattern in Javanese culture, so called

because only the ruling class was allowed to sport the

pattern on their ceremonial dress. The Parang Rusak

generally comprises of two motifs, the parang - a sword

signifying bravery and success - and the cotton plant,

which symbolizes abundance and fertility to the owner.

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Although the Parang Rusak is an important

ceremonial cloth in Indonesian tradition and culture, it is

unfortunately not as mathematically interesting as the

mandala rosette and the Kawung Picus. It is however, a

member of the frieze group. It is supposed to be a simple

frieze pattern with a vertical reflection.

The Kawung Picus

The ideal Kawung Picus should be an integration of

three motifs; a daisy-like flower motif, a circular motif

and a diamond-shaped motif. Taken as an individual motif,

the Kawung Picus has both 90o rotational symmetry and 4-

fold reflectional symmetry.

Ironically, the Kawung Picus looks like it sits more

snugly under the heading of ‘tilings’ than of ‘symmetry’

but for the sad (sob) fact that it is not made up of regular

polygons. It is however, very similar to the structure of

the 3, 4, 6, 4 tiling where a large ‘circle’ made up of

squares and triangles seem to overlap the surrounding

‘circles’ leaving a hexagon in the middle.

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