Bobbin lace is a fibre art form in which intricate and delicate patterns are created by braiding together many threads. We present an overview of the making of bobbin lace, illustrated with a simple, traditional bookmark design. We briefly summarize research on the topology of textiles and braid theory, which form a base for the current work. We then define a new mathematical model that supports the enumeration and generation of bobbin lace patterns using an intelligent combinatorial search, and which is capable of producing patterns that have never been seen before. Finally, we apply our new patterns to an original bookmark design and propose future areas for exploration.
An is a braid in which each strand alternates going over and under the strands that it crosses (see Figures c and d). Alternating braids are characterized by the property that the @math generators for even positions have the opposite sign (superscript) from the @math generators for odd positions @cite_1 . Given the generator representation for bobbin lace actions, we infer that any combination of cross and twist will result in an alternating braid.
@cite_1
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1. Introduction & Foundations. 2. The Braid Group. 3. World Problem. 4. Special types of braids. 5. Quotient groups of the braid group. 6. Isotopy of braids. 7. Homotopy braid theory. 8. From knots to braids. 9. Markov's theorem. 10. Knot invariants. 11. Braid groups on surfaces. 12. Algebraic equations. Appendix I: Group theory. Appendix II: Topology. Appendix III: Symplectic group. Appendix IV. Appendix V. Bibliography. Index.