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

TL;DR

This paper introduces a topological method that systematically generates all possible Pulli Kolam patterns for any number of dots and arrangements, bridging traditional art with mathematical topology.

Contribution

It presents a novel 5-step topological approach to create all Pulli Kolam patterns for arbitrary dot configurations, enhancing understanding of the art form through mathematics.

Findings

Systematic generation of all possible kolams for any dot number

Applicable to any spatial configuration of dots

Provides a mathematical foundation for traditional art

Abstract

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.