about Batik!

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 Influence: Central Characteristics:
focus
• leaves or buds
• animals
on
background
of
leaves
• animal and leaves
combined with the
wings
of
the
mystical
garuda
eagle
West Java: Kain Simbut made Hand drawn batik on
up of simbut figures, geometric silk organza adorned
forms like scrolls, swastikas & with prada
triangles
Central Java: Jlamprang motif Gringsing pattern is one
consists of intricate borders & of the oldest batik
edgings. (The Patula)
motifs. Period: 19th
century AD, Kingdom
of Kediri, East Java.
Gringsing motif is used
as the background. Dutch scholar Rhouffaer
Ceplok: Made up of lines that Gajah birawa, awesome
form squares, circles, slanting elephant, belongs to the
rows or other forms that are semen family of designs.
arranged
in
a
square
composition.(square patterns;
ancient temple reliefs in central
Java)
Line of symmetry: 90º
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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Mandala
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.
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’.
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.
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
normally
head
worn
cloth.
by
Good
quality
aristocratic
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selendangs
Muslim
ladies.
are
The
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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17
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.
Borders: No
symmetry
Angle of
Rotation: 180
Type: pmg
Description:
West Java: Kain
Simbut made up
of
figures
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simbut
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
¾ In Ropes
Repeated
translational
patterns as
shown below.
¾ Frieze Patterns in Iron Rod
21
22
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
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4.
This
results
in
an
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
Photo of Carved Rosette on
in
Guitar
Carvings which signify
the craftsman’s skill
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
natural
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Raspberry
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 4fold 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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