Tamils - a Trans State Nation..

"To us all towns are one, all men our kin.
Life's good comes not from others' gift, nor ill
Man's pains and pains' relief are from within.
Thus have we seen in visions of the wise !."
-
Tamil Poem in Purananuru, circa 500 B.C

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Home > Tamil Culture - the Heart of Tamil National Consciousness > Kolam: Symmetry in Threshold Design in Tamil Nadu

CONTENTS
OF THIS SECTION
22/07/09

Tile-based kolam patterns - Saty Raghavachary

Kolams of South India
The Beauty, Dynamics and Design of String Patterns in Folk Arts - Kolam Art & Science Forum (KASF), Japan Conference, 2006

Kolam Arts & Science Forum, Japan, Video Presentation


Beauty and Dynamics of Kolam


Kolams in Pondicherry

Related External Sites

Kolams at Pudukottai
Kolams at Puddukotai

Kolam - the Way

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."

Kolams von M. Kantimati - Vorgestellt von Ulrike Niklas
Mylapore Kolam Festival 2006
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..."
Kolam Generator
Vortex of Kolams
The Kolam Tradition at 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.."
Pongal Kolam Designs
Kolams in auroville
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.."
Kolam: The Divine disguised as Cosmic Pattern
Kolams - Traditional Practices
La tradici�n Kolam (Spanish)
Las figuras Kolam (Spanish)
A Portrait of the Imagination as a Malleable Kolam: K. S. Maniam's In a Far Country - Shanthini Pillai, National University of Malaysia
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.."
Kolams
Stephen P. Huyler - The Art of Worship - Kolam ritual and Hinduism in India

Kolam: Symmetry
in Threshold Design in Tamil Nadu

"..a glimpse of the richness and diversity of Tamil culture.."

Kolam Design - the Mathematics

Courtesy - Manorama Talaiver
April 25, 1995


What is threshold design?

Kolam - Threshold DesignWhen 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.


Kolam - 3,1 Points

Look at the picture. My first design was drawn using 3, 1 points.

Kolam Design

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.

Kolam - Brahama' Knot

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?

Kolam - Brahma's Knot

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?


Tile-based kolam patterns - Saty Raghavachary
DreamWorks Feature Animation
[email protected]amworks.com [also in PDF]

1 Introduction

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).

3 References

Kalyanasundaram 1999. Kolam - Artwork of South India. http://www.geocities.com/Athens/5180/kolam.html

Siromoney, G 1974. Array Grammars and Kolam. Computer Graphics and Image Processing, iii, 63-88.

Inasu, V.P. 1988. Application of L-systems to the Algorithmic Generation of Kolam Patterns. M.Tech Thesis, IIT Madras.


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    S. Nagata
    Forma, Vol. 22 (No. 1), pp. 1-3, 2007
    [Full text] (PDF 716 KB)

  • Knots, Links, and Self-Avoiding Curves
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  • Fundamental Study on Design System of Kolam Pattern
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  • Extended Pasting Scheme for Kolam Pattern Generation
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