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

This paper extends Hridaya Kolam patterns to cases where the number of dots ($m$) and arms ($n$) are not coprime, i.e., $\gcd (m,n)\mathrm{\ne }1$. 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.