Part of Splinterfields.

To me the simple act of tying a knot is an adventure in unlimited space. A bit of string affords the dimensional latitude that is unique among the entities. For an uncomplicated strand is a palpable object that, for all practical purposes, possesses one dimension only. If we move a single strand out of the plane, interlacing at will, actual objects of beauty result in what is practically two dimensions; and if we choose to direct our strand out of this plane, another dimension is added which provides an opportunity that is limited only by the scope of our own imagery and the length of a ropemakers coil.

-The Book of Knots, Clifford W Ashley

Ideas:

• museums in Brussels and Gent

http://lace.lacefairy.com/Lace/International/Brussells.html

• Creating Sorting algorithms as per e.g. http://sortvis.org/ as textiles
• macrame as large scale lacemaking (is this true?)http://www.wikihow.com/Macrame
• 10mm braid rope - multiple colours, prefer nonpatterned rope so as to let the knot patters stand out
• should it be a Research Workshop rather than a doing learning workshop?
  • Plan is that we do a series of smaller “exercises” over 1 (or 2?) days on various themes
  • 2D Symmetries in fabrics, relation to the planar symmetry groups
  • Use of symmetries, e.g. to be able to cut and still have appropriate pattern structures.
  • Hiding symmetries (esp repetitions) in textiles
  • Notational techniques in knitting and crochet, also weaving. relations to mathematical notations, procedural notations.
  • Splicing in 3 and 4 core rope. Symmetry (in end splices) and symmetry breaking (in eye splicing), the two splicing techniques
  • Parametrisation in textiles and sizes (related strongly to notation)
• Biology and mathematics?
• Knotting patterns that give emergent 3D structures (including hyperbolic_geometry): e.g. crochet→ Hyperbolic Reef (link needed).
• Given a pattern, what is the simplest algorithm to make it → Kolmogorov complexity
• Challenge: “How to learn some (nontrivial) mathematics through textiles”
• large scale 3D weaving - space filling cords.
• Museum visit at close of first day?
• Material Budget: around 700
• Dates: 3 days around the weekend of 23-25 July 2011
• Bridges Conference examples:
  • Celtic knot patterns
  • self similar knots
  • weaving: see also html version here
  • Moebius Strip knitting
• Question: are Celtic knot patterns related to Turk's Head knots?

Resources

• Lots of knots: http://www.realknots.com/
• Mathematical knitting: http://www.toroidalsnark.net/mathknit.html
• A nice article about knots, maths and textiles: http://www.yorktech.com/science/craig/Other/Knots.htm
• History of the Borromean Rings: http://www.liv.ac.uk/~spmr02/rings/
• Crafting by Concepts book; http://www.toroidalsnark.net/mkbook2.html
• The American Mathematical Society has a series of meetings: 2009,

misc:

• Brunnian rings: Nils Baas networks that unravel with a single cut.

• treemaker origami software > http://www.langorigami.com/science/treemaker/treemaker5.php4
• anarchiste origami > http://www.le-crimp.org/spip.php?page=documents&id_article=11

• algorithmic_textiles & http://fiberarts.org/design/articles/algebra.html
• requests: small frame loom + yarn