Kolam refers to drawings and patterns that women in South India (Tamil Nadu to be precise) draw in front of their homes. There is a linkage between kolam patterns and mathematical concepts such as fractals, abstract algebra and sequences. Kolam is called Rangoli in other parts of India.
Kolam designs can vary a lot in terms of sophistication and complexity. No matter what the complexity is, the foundations of Kolam designs are dots (Pulli in Tamil) and lines (Kambi in Tamil).
Kolam patterns are typically made using dry or wet rice powder. Sometimes, coloured rice powder using natural dyes are also used on festivals such as https://en.wikipedia.org/wiki/Thai_PongalPongal.
Significance of Kolam designs
Kolam has an aesthetic purpose. The need to create a welcoming and pleasing entrance for the home. The women of the house draw the kolam patterns on a wet ground so that the powder will stick to the surface and last longer. In any case, kolam patterns are drawn afresh every day.
Kolam is also meant to feed insects and birds. That's also the reason why kolam is always drawn using rice flour.
The geometric patterns that make up popular kolam designs such as the triangle and circles have meanings. The triangle facing downward represents the man while the triangle facing upwards represents the woman.
Elaborate kolam designs are drawn to signify auspisious occasions such as festivals and weddings. Women in Tamil Nadu also draw kolams in front of Hindu Temples as a form of prayer or offering to the deities.
Kolam also has a social significance. It provides an opportunity for women in the neighbourhood to collaborate and work on intricate designs or bring in an element of competition between households.
In summary, kolam is an art form that continues to hide in plain sight. This ancient practice (believed to be over 5000 years old) is so common yet it is not at the forefront of art. In spite of its less than glamorous existence, the practice of kolam designs continues to thrive in South India.
References:
https://www.quora.com/What-is-the-significance-of-the-artwork-of-Kolam-or-Rangoli-What-are-some-interesting-facts-about-themQuora
https://en.wikipedia.org/wiki/KolamWikipedia
https://www.jodilogik.com/wordpress/index.php/kolam-designs/The Jodi Logik Blog