Symmetry classification and enumeration of square-tile sikku kolams

Pulli kolam is an ancient mathematical art form that is still practiced today in south India by over a quarter million people. ‘Pulli’ in the Tamizh language means ‘dots’. A specific type of pulli kolam is sikku kolam where a series of dots are placed using rice flour and lines are drawn around them following three simple rules. Here we focus on sikku kolams assembled from square tiles. Kolams are classified by their point group symmetry and formulae are derived for counting the number of kolams of each symmetry type. Some interesting constraint problems are posed that could help formulate new games based on this elegant art form.