Knot Pattern Similar to a Lotus Kolam

leaves n

9

periods l

5

lengthen each loop

46

reducing torus and alternating crossings by third loop

conventional lines in Lotus Kolam for odd periods

9 leaves, 5 periods, 1 loop, 36 crossings

This Demonstration shows two figures. On the left is a torus knot (coil or rosette) pattern, winding a thickened curve in a spiral around a torus plotted using parametric equations.

The right graphic shows a Lotus Kolam. This variety of Kolam pattern comes mainly from Tamil Nadu, South India, and is hand drawn using a star-polygon-like framework but with different definitions (in form and process) and with more degrees of freedom. The drawings connect a dot on each adjacent radial line in sequence, and finally create a loop or multi-loop pattern.

A torus knot (without the torus) has the same topology as the Lotus Kolam. The number of components of the knot link and the loop number of the Lotus Kolam are the same as

gcd(l,n)

(in Mathematica given by KnotData["TorusKnot",{l,n}]), where

n

is the number of leaves in the Lotus Kolam or turns in the torus knot, and

l

is the number of periods in the Lotus Kolam or the torus knot.