Extending Hridaya Kolam to Multiple Loops: A Study of Non-Coprime Dot--Arm Structures

TL;DR

This paper generalizes Hridaya Kolam patterns to non-coprime dot and arm counts, introducing a modular arithmetic algorithm to generate multi-loop structures with potential applications in architecture and design.

Contribution

It presents a novel algorithm for creating multi-loop Hridaya Kolam patterns when dots and arms are not coprime, expanding the design space of traditional patterns.

Findings

Algorithm successfully generates multi-loop Kolam patterns.

Patterns demonstrate complex multi-loop structures for various non-coprime pairs.

Potential applications in architectural motifs and ornamental designs.

Abstract

This paper extends Hridaya Kolam patterns to cases where the number of dots ($m$) and arms ($n$) are not coprime, i.e., $\gcd(m, n) \ne 1$. Such configurations give rise to multiple disjoint closed loops. We propose a modular-arithmetic-based algorithm to systematically generate such patterns, and illustrative patterns for various non-coprime $(m, n)$ pairs are provided to demonstrate the resulting multi-loop structures. These multi-loop Kolam designs can inspire architectural motifs and ornamental patterns in floor plans, facades, and decorative elements.