Developing a Mathematical Model for Bobbin Lace

TL;DR

This paper introduces a new mathematical model for generating and enumerating bobbin lace patterns, leveraging braid theory and combinatorial search to discover novel designs and apply them to practical artifacts.

Contribution

The paper develops a mathematical model that enables systematic generation and discovery of new bobbin lace patterns using combinatorial and topological methods.

Findings

Model reveals new, previously unseen lace patterns

Successfully applied new patterns to a bookmark design

Demonstrates the model's effectiveness in pattern enumeration

Abstract

Bobbin lace is a fibre art form in which intricate and delicate patterns are created by braiding together many threads. An overview of how bobbin lace is made is presented and illustrated with a simple, traditional bookmark design. Research on the topology of textiles and braid theory form a base for the current work and is briefly summarized. We define a new mathematical model that supports the enumeration and generation of bobbin lace patterns using an intelligent combinatorial search. Results of this new approach are presented and, by comparison to existing bobbin lace patterns, it is demonstrated that this model reveals new patterns that have never been seen before. Finally, we apply our new patterns to an original bookmark design and propose future areas for exploration.