Kolam - Chantal
Jumel in French
and also in
English "With the ground as
the means of expression, the hand for sole
instrument and coloured powders, the Tamil
k�lam rests on a dual language,
that of silence and humility and of symbolic
writing, the gate which opens to the realm of
imagination. In Tamil-Nadu, it is the women of all
communities and all faiths together who draw on the
ground."
Kolam - That
which feeds the eyes, feeds the soul "In the summer of 2004, Srimati
Shyamala of Chennai shared with us the kolam
practices of South India. A different kolam design is
drawn for each day of the week. Each mandala honors
the planet that rules over that day. The symbols and
patterns that are used are specific to each planet
and presiding deity of that day and create a visual
prayer, benefiting all who pass by it.
.."
Kolam Interactive "..Generally, a
kolam is drawn with bare fingers using predetermined
dots...This tradition of decorating with kolams is
passed on from generation to generation. ikolam.com
is an interesting attempt at preserving this
important custom. ikolam.com interactively shows the
steps involved in drawing a kolam..."
The Kolam
Traditionat American
Scientist"..The women of
Tamil Nadu in southeastern India traditionally cover
their thresholds every morning with elaborate designs
drawn with rice powder. Girls learn the ritual from
their mothers and other female relatives, and kolam
skills are considered a mark of grace, dexterity,
discipline and concentration. Drawing the kolam
figures is an important part of the Tamil Nadu
culture and landscape. But with their orderly and
often highly symmetrical designs, which frequently
group into families, kolams are also expressive of
mathematical ideas. In the last few decades, kolam
figures have attracted the attention of computer
scientists interested in describing images with
picture languages. Different picture languages have
been developed to describe different kolam
families..."
Kolam- Art Work of
India"Kolam refers
to decorative artwork drawn on the floor in front of
houses and in front of deities in puja rooms. Most
often finely ground rice flour is used to make these
drawings on wet/moist ground previously sprinkled
with water (even dilute solutions of cow-dung cake
that gives a darker background to the mud floor).
Coloration of the artwork with color powders adds
additional charm. It is a time old cultural tradition
of south indian families going back to many many
generations..."
South Indian Kolam
Patterns - Dr.Gift Siromoney"..Any one
traveling through rural Tamil Nadu during the months
of December and January will be richly rewarded by
the sight of a variety of patterns decorating the
courtyards of even the humblest of homes ...The three
main classes of kolam recognized in computer
mathematics10 are the Finite Matrix Kolam,
the Regular Matrix Kolam and the Context-free Regular
Array Kolam..."
Kolam at Kamat's Potpourri
"..Typically laid with rice powder, Kolam is a
women's art in South India with spiritual
connections.."
Kolams in Auroville"..a glimpse of the richness and
diversity of Tamil culture.. The 'kolam' is a
symbol of an open heart and an auspicious welcoming.
Its colourful, devotional presence in the villages in
the Auroville area is a well appreciated and
respected feature, and we're happy to share some of
its touch with you through this page...Until recent
times, kolams were most often drawn with coarse rice
flower, thus serving as a conscious offering to
nature's creatures. Rice flower is seen as an
offering to Lakshmi, the goddess of rice. In south
India, where wealth is measured in terms of rice
fields, Lakshmi plays an essential caretaker role to
assure the family's continued existence and survival.
The goddess has the power to attract wealth and
prosperity and to prevent poverty from entering the
home. Today, especially where rice is expensive,
kolams are made of powered limestone, red soil or
chalk. In some regions salt, turmeric powder,
flowers, rocks, stones and sawdust are also used.
Some women cannot resist the more colourful
store-bought artificial chalk power tints and the
technicolour world of magentas, emerald greens,
turquoise and cobalt blues. Plastic sticker kolams
are also used and herald city life and a different
set of priorities for a woman's time.."
Kolams"The
'kolam' is a symbol of an open heart and an
auspicious welcoming. Its colourful, devotional
presence in the villages in the Auroville area is a
well appreciated and respected feature, and we're
happy to share some of its touch with you through
this page.."
"..a glimpse of the richness
and diversity of Tamil culture.."
Courtesy - Manorama
Talaiver
April 25, 1995
What is threshold design?
When I was a little
girl, my aunt used to get up early in the
morning. She would have a shower and then created
a symmetrical pattern in the front yard, after
cleaning and sprinkling water. Some women in
Madras still create these designs. I must admit
that I had to drive ten miles from downtown
before I found a row of houses with the threshold
design. These patterns are normally called
"Kolum." O sounds like Oh. U sounds like bun.
Kohlum. When the symmetrical pattern is decorated
in colors using colored sand or flower, then it
is called rangoli.
The design or pattern is not symmetrical
sometimes, but it is just a continuous line that
curves around to make a beautiful border or
design at the Center of the yard. . The threshold
desing is compared to African sand drawings.
These patterns or designs were created in the
olden days (according to Tamil literature) using
rice flour. Holding a handful of flour in their
right hand, the woman will uniformly drop the
flour to make a line through her thumb and
pointer and keep on moving her hands to make the
curve or the dots. Nowadays, women use powder
made out of stone. (Stone is crushed and sold
commercially).
The patterns are very complicated and huge
during festival months. The temples will have
complex patterns that will cover thousands of
square feet. Sometimes, several women together
will create one large design. As a child, I have
always wondered at the complexity of the pattern
and the creativity of the women.
The pattern normally starts with putting the
dots as follows:
.
. . .
. . . . .
. . . . . . .
. . . . .
. . .
.
This is a very simple design. You
start with seven dots in the middle and you skip
two to count down. Then, you will use your
creativity to circle around the dots (in most
cases) or connect the dots (rarely). When a
mother is creating this design, a girl tends to
watch this from the time she is a
baby.
My thesis is number concept comes very
naturally to girls by observing. When the girl
grows up, girls have competitions on who can
create a complex pattern and with maximum number
of points. Skip count, multiplication, geometric
design, function concept and concept of closed
curves - all of these can be introduced in math
classrooms using the threshold. Based on the
concept of Kolum, I will be providing lessons
here that can be used in math classrooms.
A multicultural Mathematics lesson for
Elementary Grades
Objectives:
1. To discuss the life of a little third
grader in the morning while she watches her mom
doing the symmetrical design.
2. To draw a simple symmetrical design as given
in this page.
3, To extend this design to a larger number of
points.
4. To create other designs for odd number of
points.
5. To explore the design differences that can
affect symmetry with the use of odd and even
number of points.
Materials needed:
pencil, paper, crayon, (if you are bold, try
rice flour in the kitchen floor) Procedure.
Look at the picture. My first design was drawn
using 3, 1 points.
My second design was drawn using 5,3,1
points.
My third design was done with 7,5,3,1.
Practice the symmetrical design.
Extend the design to 9 points.
Questions:
How can you extend this further?
When you create the design for larger number
of points, what can you infer from the
patterns?
Extension:
The next pattern is called Brahma's knot. This
design is more complicated to draw.
This is the first level of Brahma's knot
Can you draw this on a sheet of paper?
This is the second level of Brahma's' knot
Can you try the second level?
Now a challenge
What is the next level of Brahma's knot?
Can you draw the design and fax it to me?
These were some designs on the pavement in
front of a house. These are permanent. These were
not created with flour but with paint.
Slowly the tradition of creating threshold
design seems to disappear. After five days of my
travel in South India, I found this woman
creating the threshold design in front of her hut
early morning. I hope this tradition that I love
and appreciate continues for ever! I found a few
houses with permanent designs in the cities. This
means that the women do not create the designs
every day. They use white paint to create
permanent designs.
Something to think about! I was
surprised to hear about gender differences in
mathematics achievement when I first arrived in
the United States.
In India, gender differences and related
discussions exist about career choices. Female
children are normally advised to become teachers,
bank tellers, or even bank officers. However,
this is not true today.
I have never heard a mother telling a girl,
"Oh well, you are a girl. You cannot do math." Or
I have never heard a teacher talking about gender
differences in mathematics achievement.
In my school days, girls scored better in all
classes than boys. The names of the top five
scorers were listed on the blackboard in my
classroom every month. When I was a student, two
or three of my girl friends including myself were
always listed among the top five in math
classes.
My conviction is that number concepts come
naturally to girls in South India. I have no
research to support this statement. However, I
can argue that the girls watch the mothers
create the threshold design in the front yard
or in the kitchen. These designs involve
numbering, skip counting, symmetry and so on.
Is it possible for me to say then that
arithmetic or logic is part of a girl's life in
India?
Kolams are centuries-old line patterns drawn
at the thresholds of homes in Southern India. The
figure below shows an example. The drawings are
constructed from white flour or powdered
limestone and have ornamental as well as
religious significance in the Hindu tradition
[Kalyanasundaram 1999]. The dot grid is laid down
first, then the pattern is drawn in continuous
loops which wind around the dots.
This sketch presents a set of 16 decorated
tiles which serve as an alternate way to
construct kolams. To the best of the
author�s knowledge, this is a
novel approach. Existing characterizations of
kolams have been in terms of two-dimensional
picture grammars [Siromoney 1974] or L-systems
[Inasu 1988]. Also, children are taught kolams
using the dot-grid, curve-based continuous
drawing technique used by adults, which makes it
difficult to memorize them or create variations.
Tile-based construction instead offers an
inviting approach more suitable for
experimentation.
2 Tile-based construction
Pictured below is a typical progression in the
construction of the kolam shown above. The curve
(just a single closed loop in our case) carefully
meanders through the spaces in between the dots,
creating a pleasing arrangement of overlapping
segments.
Instead of being drawn in a continuous manner,
the same kolam can be generated in a completely
different way, using diamondshaped tiles placed
corner to corner (not close-packed). The
following image shows how. Each tile has markings
on it (including a dot at the center), and an
assembly of tiles with appropriate decorations
creates the kolam when their piecewise markings
link up to reproduce the overall curves.
It turns out that exactly 16 tiles are all
that are necessary to capture the endless variety
of kolams. The complete tile catalog is shown
below. The topmost row contains an
�empty� tile
with all four corners free. The other rows show
tiles with one, two, three and four corners
�occupied� by
decorations. Combinatorially, this is yields the
set of C(4,0)+C(4,1)+C(4,2)+C(4,3)+C(4,4)=16
tiles. Creating valid kolams now becomes a matter
of choosing adjacent tiles so that mating corners
have curve segments crossing over (no dangling
curves). This makes it amenable to algorithmic
exploration using techniques borrowed from
tessellation research.
Shown below is a more complex kolam that
employs 15 out of the 16 pieces from the set (all
except the last piece).
Preface: The Beauty, Dynamics, and Design
of String-Patterns in Folk Arts
S. Nagata Forma, Vol. 22 (No.
1), pp. 1-3, 2007 [Full text](PDF 716 KB)
Knots, Links, and Self-Avoiding
Curves
S. Jablan and R. Sazdanovic Forma, Vol. 22 (No.
1), pp. 5-13, 2007
[Abstract] | [Full text](PDF 524 KB) |
[Attractive image
Fig.9,
Fig.11, 12]
Solving Infinite Kolam in Knot
Theory
Y. Ishimoto Forma, Vol. 22 (No.
1), pp. 15-30, 2007
[Abstract] | [Full text](PDF 848 KB) |
[Attractive image
Fig.3,
Fig.4]
Fundamental Study on Design System of
Kolam Pattern
K. Yanagisawa and S. Nagata Forma, Vol. 22 (No.
1), pp. 31-46, 2007
[Abstract] | [Full text](PDF 568 KB) |
[Attractive image
Fig.11,
Fig.13,
Fig.20]
P Systems for Array Generation and
Application to Kolam Patterns
K. G. Subramanian, R. Saravanan and T.
Robinson Forma, Vol. 22 (No.
1), pp. 47-54, 2007
[Abstract] | [Full text](PDF 96 KB) |
[Attractive image
Fig.4,
Fig.5, 6]
Extended Pasting Scheme for Kolam Pattern
Generation
T. Robinson Forma, Vol. 22 (No.
1), pp. 55-64, 2007
[Abstract] | [Full text](PDF 796 KB) |
[Attractive image
Fig.6,
Fig.7,
Fig.10]
Hierarchical Modular Systems with Elements
of Folk Art
N. Kishimoto and M. C. Natori Forma, Vol. 22 (No.
1), pp. 65-74, 2007
[Abstract] | [Full text](PDF 556 KB) |
[Attractive image
Fig.2,
Fig.3, 4]
A Space-filling Three-dimensional Serial
Polyaxis
R. Oka and M. Kawamoto Forma, Vol. 22 (No.
1), pp. 93-102, 2007
[Abstract] | [Full text](PDF 880 KB) |
[Attractive image
Fig.3,
Fig.4,
Fig.5]
Analysis of Impression from Geometric
Patterns in Textiles of Cultural Properties
in Japan
K. Goto, A. Goto, A. Nakai, M. Sato, K.
Morimoto and H. Hamada Forma, Vol. 22 (No.
1), pp. 103-111, 2007
[Abstract] | [Full text](PDF 6.3 MB) |
[Attractive image
Fig.1,
Fig.3,
Fig.6]
PsyKolo3D-Interactive Computer Graphical
Content of "Kolam" Design Blocks
Y. Kawai, K. Takahashi and S. Nagata Forma, Vol. 22 (No.
1), pp. 113-118, 2007
[Abstract] | [Full text](PDF 1.7 MB) |
[Attractive image
Fig.1,
Fig.3,
Fig.10(animation)]
Letter Digitalization and Analysis of Traditional
Cycle Patterns in the World, and Their
Contemporary Applications
S. Nagata Forma, Vol. 22 (No.
1), pp. 119-126, 2007 [Full text](PDF 1.3 MB) |
[Attractive image
Fig.1,
Fig.4(animation),
Fig.8]
Forum Drawing Down Desires: Women, Ritual and
Art in Tamil Nadu
V. Nagarajan Forma, Vol. 22 (No.
1), pp. 127-128, 2007 [Full text](PDF 244 KB) |
[Attractive image
Fig.1]
Forum African Sona, Mirror Curves and
Lunda-Designs
P. Gerdes Forma, Vol. 22 (No.
1), pp. 129-131, 2007 [Full text](PDF 44 KB) |
[Attractive image
Fig.2, 3]
Forum Analysis of Spiral Curves in Traditional
Cultures
R. Takaki and N. Ueda Forma, Vol. 22 (No. 1),
pp. 133-139, 2007
[Abstract] | [Full text](PDF 884 KB) |
[Attractive image
Fig.1,
Fig.2,
Fig.4]
When I was a little
girl, my aunt used to get up early in the
morning. She would have a shower and then created
a symmetrical pattern in the front yard, after
cleaning and sprinkling water. Some women in
Madras still create these designs. I must admit
that I had to drive ten miles from downtown
before I found a row of houses with the threshold
design. These patterns are normally called
"Kolum." O sounds like Oh. U sounds like bun.
Kohlum. When the symmetrical pattern is decorated
in colors using colored sand or flower, then it
is called rangoli.
