Quasiperiodic bobbin lace patterns

TL;DR

This paper introduces a mathematical framework for creating non-periodic bobbin lace patterns, expanding traditional designs by incorporating quasiperiodic structures like Sturmian words and Penrose tilings.

Contribution

It establishes the foundational theory for quasiperiodic lace patterns and presents three novel pattern families based on advanced mathematical tilings and sequences.

Findings

Developed quasiperiodic lace pattern families

Extended traditional periodic lace design principles

Provided mathematical models for complex lace patterns

Abstract

Bobbin lace is a fibre art form in which threads are braided together to form a fabric, often with a very detailed and complex design. In traditional practice, each region of the fabric is filled with a periodic texture. We establish the groundwork for non-periodic lace patterns and present three new quasiperiodic families based on Sturmian words, the Penrose tiling by thick and thin rhombs and the Ammann-bar decoration of the Penrose tiling.