Extending Hridaya Kolam to Even-Ordered Dot Patterns and Their Applications

TL;DR

This paper generalizes Hridaya Kolam patterns to even-ordered dot arrangements using modular arithmetic, revealing new cyclic sequences and symmetries, and translating these mathematical insights into contemporary textile art.

Contribution

It introduces a novel mathematical framework for even-ordered kolam patterns, expanding the classical scope and providing explicit algorithms for their construction.

Findings

New cyclic sequences for even-ordered kolam patterns

Identification of symmetries and structural properties

Application of patterns in contemporary textile art

Abstract

This study extends the mathematical framework of Hridaya Kolam patterns by applying modular arithmetic to even-ordered dot arrangements with arm counts co-prime to the number of dots. We analyze the resulting cyclic sequences that correspond to Eulerian circuits, enabling continuous single-stroke kolam designs beyond the classical odd-ordered cases. Our method provides explicit algorithms for constructing these intricate patterns, unveiling new symmetries and structural properties. Elevating this traditional floor art, we translate these mathematically grounded motifs into striking designs, showcasing their beauty and complexity in contemporary dari art in the carpet and textile sectors.