A Topological Approach to Creating any Pulli Kolam, an Artform from Southern India

Pulli kolam is a ubiquitous art form in south India. It involves drawing a line looped around a collection of dots (pullis) place on a plane such that three mandatory rules are followed: all line orbits should be closed, all dots are encircled and no two lines can overlap over a finite length. The mathematical foundation for this art form has attracted attention over the years. In this work, we propose a simple 5-step topological method by which one can systematically draw all possible kolams for any number of dots N arranged in any spatial configuration on a surface.Comment: 10 pages, 11 figures, version 2 has corrected Fig. 10, and added a new figure 11. Discussion following Eq. 1 has been modified. Figure 3 has been modified to generalize the type of bonds to beyond 3 types; one of the three mandatory (M) rules for forming a kolam has been clarifie