Kolam Simulation using Angles at Lattice Points

TL;DR

This paper introduces a new encoding scheme for Kolam patterns based on angular movements at lattice points, enabling simulation and generation of these geometric art forms through a computational approach.

Contribution

It proposes a novel angular encoding method for Kolam patterns and demonstrates their simulation using a Python software implementation.

Findings

Successful encoding of Kolam patterns into sequences of symbols

Simulation of Kolam patterns using turtle graphics in Python

Potential for automated generation of Kolam designs

Abstract

Kolam is a ritual art form practised by people in South India and consists of rule-bound geometric patterns of dots and lines. Single loop Kolams are mathematical closed loop patterns drawn over a grid of dots and conforming to certain heuristics. In this work, we propose a novel encoding scheme where we map the angular movements of Kolam at lattice points into sequences containing $4$ distinct symbols. This is then used to simulate single loop Kolam procedure via turtle moves in accordance with the desired angular direction at specific points. We thus obtain sequential codes for Kolams, unique up to cyclic permutations. We specify the requirements for the algorithm and indicate the general methodology. We demonstrate a sample of Kolams using our algorithm with a software implementation in Python.