Kavitha Shivan – Unlocking the Fractal Knots – Kolam

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When numbers take on a visual form, the act of creation becomes a calculated activity, informing the art and the context it holds within. Vivifying the abstract concept of numbers is a self-discovering process for me. My explorations in designed-art, or art that has been deliberated upon, has unleashed a certain sense of abandonment in understanding the extremes of birth and death, creation and destruction, and the insignificant smallness of the self in comparison to the significant magnificence of the universe. A soft awakening of the inner being while annihilating the ego, is the sort of liberation that feels like merging with the light.

‘Pattern’ and ‘Matrix’ trace their roots to the words ‘pater’-father, and ‘mater’-mother, forming the crux of all creation. Mathematics becomes the foundation of creative genesis, for both conscious and unconscious art created by humans. Touching upon the resonance of numbers seen in the golden ratio innate in the creation of a sunflower centre, a pine cone, an artichoke, a shell, or perhaps a cauliflower, for the ones who observe and connect the dots, the big revelation of our relationship with the universe is unmissable.

Fig 1 Quadrivia
Fig 1 Quadrivia

The quadrivia of number, geometry, cosmology, and music, are born out of time, matter, light, and sound (Fig. 1), and I have come to understand how the human mind does not limit itself in understanding the science of numbers and order in geometry in relation to this. As an artist and a designer, while the finite and symmetry appeals to the designer in me, the asymmetry holds in it the spark of infinite magnetism entertaining the artist within. The opposites that attract form a flux of energy that identifies with the universe. The artist then, is the entertainer, and the one entertained, filling the world full of goodness.

Observing the stars on a clear night have had me question if there is some structure and discipline in the way they are scattered. While the mind is in search of order in seeing constellations as identifiable shapes, the multi-dimensional self knows that this is a one-point-perspective that will distort in view when seen from another angle. Evolution has taught us human species to invent a better way of understanding each other as a means of survival, share the knowledge gained, and speak a language that originated in the eerie silence before the primordial sound. The reverberations of the big bang has not died yet, as we know the universe is expanding. The sound of the universe heard in the conch of the shell held close to the ears wakes me up silently, meditating upon the play of numbers in the art that I create. Isn’t sound, after all, the origin of creation?

I draw inspiration from the age old practice of using rice powder to draw Kolams on the floor outside the thresholds of homes in South India, creating mathematically aesthetic patterns laid upon intricate dotted matrices. The dance of the feet and hand that draw the Kolams in precise designs is an immensely satisfying kinetic art in space and time. Straight and curved lines continue to sinuously turn, twist, and form loops around dots that guide the pattern, in counts that increase or decrease geometrically as the artist discerns. These linear strings of art are mathematical interpretations of the universe, when they complete themselves in connecting the end to the beginning, coming a full circle. The number of initial dots laid out determine the nature of the Kolam, and the design possibilities are infinite while attempting to create the final Kolam pattern. The Kolam then turns into a fine rendering of the artist’s vision of numerical representations of time, matter, light, and sound.

Examining the Kolams in detail, we learn that the simplest of them is formed by strings that weave about precisely laid dots. The Kolams can either be looped around the dots, or connect the dots, assuming straight and curved lines. The shapes generated can be spiral, rhomboid, radial, tessellated, square, or amoeboid in nature. Starting out as single dots, and progressing to form a matrix of odd or even number of dots (Fig. 2a), there are two basic rules that are followed in creating a Kolam: all linear strings must close to completion, and all dots must be encircled or connected (Fig. 2b). The basic Kolam looks like a simple design that can attain complexity by scaling up exponentially, displaying symmetry and asymmetry growing organically, and fractally. It has order within the chaos when forming a large arrangement. When Kolams synchronise with the Fibonacci numbers, forming square grids of 32, 52, 82, 132, 212, 342 or rectangle grids of 2×3, 3×5, 5×8, 8×13, 13×21, they become modular building blocks creating a pattern that fall within the golden ratio. (Fig. 2c).


The purpose of drawing a Kolam is to invoke the positive vibrations, energy, and frequency, of the apparent visual manifestation of the homophonic chantings made by nature, and simulated by ancient humans. Appearing across primitive cultures as sand drawings, they are seen to coincide with the sound waves that are created in cymatics, and has been demonstrated in experiments seen in Chladni plates.

Primordial Rhythm (Fig. 3)

This Kolam starts with an odd dot matrix of 21 dots across, a Fibonacci number, decreasing by two on either side and ending in 1 dot. It exhibits diagonal symmetry and a square that symbolises the earth.

Cosmic Lotus (Fig. 4)

A beautiful single string of radial lotus petals overlapped by individual loops over another layer – this pattern rings in the celestial movement of planets when their paths cross.

Aumkara Trellis (Fig. 5)

The primordial sound of Aum translated into a universal visual language – an intersection of tessellations forming an aesthetic order.

Celestial Tesserae (Fig. 6)

The cardinal directions represented by snakes that coil and intertwine to form a knot. Perhaps a metaphor of cosmic origins of human existence on earth.

Naga Knot (Fig. 7)

A single loop of a snake pattern. The Indian and Celtic Snake (Fig. 8) is a comparative visual connection to the concept of the celestial knots similar across cultures.

Sun Moon (Fig. 9)

A radial Kolam representing the male and female energies, in the form of the sun and the moon.

I see Kolams as symbolic patterns of energy fields that match the frequency of primordial euphonics from the time of the creation of the universe. I question their origins, and imagine they could have been large scale patterns that materialised on desert sands or soil as an aftermath of a tremor or fault slip, settling down as visible design in the calm after the event. The answers lie in knowing the unknown, and exploring beyond what the human senses can perceive. The realm of the artist therefore extends far and wide, seeking inspiration from the mathematical creation of the universe.

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