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== Thread Geometry == | == Thread Geometry == | ||

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We explored what kind of geometric constructions we can do with thread, chalk and the help of several people... | We explored what kind of geometric constructions we can do with thread, chalk and the help of several people... | ||

− | |||

=== We found out... === | === We found out... === | ||

− | |||

* how to draw a line | * how to draw a line | ||

* how to draw a circle ( d = const.) | * how to draw a circle ( d = const.) | ||

Line 14: | Line 9: | ||

* how to measure the circumference of a circle | * how to measure the circumference of a circle | ||

* how to calcualte pi using only thread (See also [https://twitter.com/astonishedstag/status/720114478768070658 here]) | * how to calcualte pi using only thread (See also [https://twitter.com/astonishedstag/status/720114478768070658 here]) | ||

− | |||

=== 3D thread geometry === | === 3D thread geometry === | ||

− | |||

We explored how our thread-based drawing tools could be used to identify points on the surface of shapes in 3 dimensions. | We explored how our thread-based drawing tools could be used to identify points on the surface of shapes in 3 dimensions. | ||

− | |||

* We discovered the 3d ellipsoid (a + b = const.) | * We discovered the 3d ellipsoid (a + b = const.) | ||

* We found that multifocal 3d ellipsoids have a doughnut-topology. | * We found that multifocal 3d ellipsoids have a doughnut-topology. | ||

Line 24: | Line 16: | ||

** the polygon method, where the thread forms a polygon going through the focal points and the drawing point | ** the polygon method, where the thread forms a polygon going through the focal points and the drawing point | ||

** the star method where the thread is alternately visiting each focal point and the drawing point | ** the star method where the thread is alternately visiting each focal point and the drawing point | ||

− | |||

=== Observations === | === Observations === | ||

− | |||

* Geometric knowledge from school only got us so far ... | * Geometric knowledge from school only got us so far ... | ||

* There is a whole universe of "new" shapes and forms | * There is a whole universe of "new" shapes and forms | ||

− | |||

=== Questions raised === | === Questions raised === | ||

− | |||

* Questions regarding surface of different shapes popped up | * Questions regarding surface of different shapes popped up | ||

* We discussed different methods of measuring the surfaces using thread | * We discussed different methods of measuring the surfaces using thread | ||

− | |||

=== Homework === | === Homework === | ||

− | |||

* What could an Experimentier-Baukasten / a kit / a sandbox for computing with thread look like?<br>Do some research on other kinds of kits! | * What could an Experimentier-Baukasten / a kit / a sandbox for computing with thread look like?<br>Do some research on other kinds of kits! | ||

* Do some thread-based geometry at home. Pick a parameter such as the thread-length and vary it systematically | * Do some thread-based geometry at home. Pick a parameter such as the thread-length and vary it systematically | ||

* Document your thread-art in the wiki | * Document your thread-art in the wiki | ||

− | |||

=== Links === | === Links === | ||

=== Geometry === | === Geometry === | ||

Line 77: | Line 62: | ||

* [http://www.instructables.com/id/Make-a-Kumihimo-Disk-Out-of-a-CD/ How to make a Kumihimo Disk out of a CD] (braiding) | * [http://www.instructables.com/id/Make-a-Kumihimo-Disk-Out-of-a-CD/ How to make a Kumihimo Disk out of a CD] (braiding) | ||

== Knots and Splices == | == Knots and Splices == | ||

+ | === Knot History === | ||

+ | * various knot books online and offline | ||

+ | * We learned how ropes are made in a "Seilerei" on the "Reeperbahn" | ||

+ | * We learned about a rope inspection machine, that travels along a the cable of a "Seilbahn" | ||

+ | === Knot Theory === | ||

+ | * We learned the basics of knot theory | ||

+ | * Minimum number of crossings | ||

+ | * Knot-Invariants and Knot-Polynomials | ||

+ | === Knot Classification Game === | ||

+ | We played a knot identification game.<br> | ||

+ | It goes like this:<br> | ||

+ | * Student A creates two knots using thread. | ||

+ | * Student B tries to figure out whether or not the two knots are the same | ||

+ | === Homework === | ||

+ | Create a nice framework for displaying knots.<br> | ||

+ | The framework can be physical, graphical or computational in nature | ||

=== Links === | === Links === | ||

==== How are threads made? ==== | ==== How are threads made? ==== | ||

* [http://www.arte.tv/guide/de/048353-025-A/xenius Seilforschung: Wie sieht das optimale Seil aus?] | * [http://www.arte.tv/guide/de/048353-025-A/xenius Seilforschung: Wie sieht das optimale Seil aus?] | ||

==== Thread Games ==== | ==== Thread Games ==== | ||

+ | * [https://archive.org/details/cu31924029861469 String figures: a study of cat's-cradle in many lands] | ||

==== Self-Assembly ==== | ==== Self-Assembly ==== | ||

* [http://news.rice.edu/2016/04/14/nanotubes-assemble-rice-introduces-teslaphoresis-2/ Teslaphoresis] (self-assembly of threads) | * [http://news.rice.edu/2016/04/14/nanotubes-assemble-rice-introduces-teslaphoresis-2/ Teslaphoresis] (self-assembly of threads) | ||

* Spontaneous Patterns in vibrated Ball Chains: [http://www.maths.bris.ac.uk/~majge/hjce.06.pdf Knots] and [http://cnls.lanl.gov/~ebn/pubs/spiral/spiral.pdf Spirals] | * Spontaneous Patterns in vibrated Ball Chains: [http://www.maths.bris.ac.uk/~majge/hjce.06.pdf Knots] and [http://cnls.lanl.gov/~ebn/pubs/spiral/spiral.pdf Spirals] | ||

==== Knotting ==== | ==== Knotting ==== | ||

+ | * [https://issuu.com/grupo.scout.nomadas.wfis.spain/docs/1998_turner___griend_history_and_sc History and Science of Knots] | ||

* [http://www.animatedknots.com/ Animated Online Encyclopedia of Knots] | * [http://www.animatedknots.com/ Animated Online Encyclopedia of Knots] | ||

* Encylopedia of Knots and Fancy Rope Work ISBN 978-0870330216 | * Encylopedia of Knots and Fancy Rope Work ISBN 978-0870330216 | ||

Line 98: | Line 101: | ||

* [https://www.youtube.com/watch?v=aqyyhhnGraw&list=PLt5AfwLFPxWLyfD4nhZCX_3UZdSSpkBTs&index=1 Knot Theory Videos] by Numberphile | * [https://www.youtube.com/watch?v=aqyyhhnGraw&list=PLt5AfwLFPxWLyfD4nhZCX_3UZdSSpkBTs&index=1 Knot Theory Videos] by Numberphile | ||

* [https://www.youtube.com/watch?v=co78AEqsv3s How Mathematics gets into Knots] | * [https://www.youtube.com/watch?v=co78AEqsv3s How Mathematics gets into Knots] | ||

− | * Alexei Sossinsky, ''Mathematik der Knoten: Wie eine Theorie entsteht'' ISBN 978-3499609305 | + | * Alexei Sossinsky, ''Mathematik der Knoten: Wie eine Theorie entsteht'', ISBN 978-3499609305 |

* [http://katlas.org The Knot Atlas] | * [http://katlas.org The Knot Atlas] | ||

+ | * [http://katlas.org/wiki/Other_Knot_Tables Historic Knot Tables] | ||

+ | ==== Tie Knotting ==== | ||

+ | * [https://peerj.com/articles/cs-2/ More Ties than we thought] (paper) | ||

+ | * [http://tieknots.johanssons.org/ random tie knot generator] | ||

+ | ==== Bondage ==== | ||

+ | * [[wikipedia:Hojōjutsu|Hojōjutsu]] japanese martial arts technique | ||

+ | * [http://tracks.arte.tv/de/shibari-oder-die-kunst-des-bondage Shibari] arte documentary on japanese bondage | ||

+ | * [http://go-get-knotted.tumblr.com Go get knotted] a blog to learn bondage knots | ||

+ | * [http://www.garthknight.com/portfolios/2012enchantedforest/ Enchanted Forest] photo series by Garth Knight | ||

==== Knot Robot ==== | ==== Knot Robot ==== | ||

* [http://www.ritsumei.ac.jp/se/~hirai/research/linearobjectmanipulation-e.html Manipulation of Deformable Linear Objects] feat. [https://www.youtube.com/watch?v=UZfpFkIdhl0 Un-Knotting Bot] | * [http://www.ritsumei.ac.jp/se/~hirai/research/linearobjectmanipulation-e.html Manipulation of Deformable Linear Objects] feat. [https://www.youtube.com/watch?v=UZfpFkIdhl0 Un-Knotting Bot] | ||

* [http://ijr.sagepub.com/content/25/4/371.full.pdf Knotting/Unknotting: Manipulation of Deformable Linear Objects] | * [http://ijr.sagepub.com/content/25/4/371.full.pdf Knotting/Unknotting: Manipulation of Deformable Linear Objects] | ||

+ | == Braids == | ||

+ | In this class we identified the basic elements of braids, and explored the intersection of braiding and sorting algorithms. | ||

+ | === Communication game === | ||

+ | * We developed and discussed different notations for braiding | ||

+ | * We played a game involving three persons | ||

+ | ** The first person creates a braid | ||

+ | ** The second person describes the structure or construction of the braid using words only | ||

+ | ** The third person recreates the braids accordingly | ||

+ | ==== Observations ==== | ||

+ | * There are different ways to describe the structure of a braid | ||

+ | ** structure vs construction | ||

+ | ** position-based vs thread-based | ||

+ | * Some instructions will not result in a braid | ||

+ | * Some systems are simpler than others, but may not be universal in the sense that they can describe every possible braid | ||

+ | === Sorting Braids === | ||

+ | * We discussed why sorting is an important topic in computer science | ||

+ | * We got to know the concept of computational complexity and the big-o notation | ||

+ | * We re-enacted several sorting algorithms using threads and chalk | ||

+ | * We developed collaborative sorting algorithms resulting in braids | ||

+ | ==== Observations ==== | ||

+ | * Bubblesort is a fun collaborative activity | ||

+ | * The mapping from sorting operations to operations of textile construction is important | ||

+ | * If the mapping is bad the result may not be a stable (overs and unders) | ||

+ | * If the mapping is bad the result may not be dense (no-ops vs crossings) | ||

+ | * Sorting networks allow for parallel sorting / braiding | ||

+ | === Links === | ||

+ | ==== Braiding ==== | ||

+ | * [https://www.flickr.com/photos/taffeta/8201660840/in/album-72157632050570535/ French Children's book] feat. Maypole Dance + Track Diagram | ||

+ | * [https://issuu.com/thepetflakesproject/docs/petflakesthebook Pet Flakes] Architecture inspired by Maypole braiding | ||

+ | * [http://weeklyweaves.blogspot.de/2014/08/bobbin-dancing-yan-tan-tethera-part-1.html Bobbin Dance] by Shane Waltener | ||

+ | ==== Sorting ==== | ||

+ | * [https://www.youtube.com/watch?v=LOxfdsBBjKI Sorting Networks] by Computer Science Unplugged | ||

+ | * [https://www.youtube.com/watch?v=lyZQPjUT5B4 Bubble Sort] as hungarian folk dance | ||

+ | * [https://www.youtube.com/watch?v=8Kp-8OGwphY Bubble Sort] | ||

+ | * [https://www.youtube.com/watch?v=EeQ8pwjQxTM Merge Sort] | ||

+ | * [https://www.youtube.com/watch?v=DFG-XuyPYUQ Insertion Sort] | ||

+ | * [https://www.youtube.com/watch?v=aQiWF4E8flQ Quick Sort] | ||

+ | ==== Computational Complexity ==== | ||

+ | * [https://www.youtube.com/watch?v=-Eiw_-v__Vo Big-O-Notation] | ||

+ | * [http://bigocheatsheet.com/ Big-O-Cheatsheet] | ||

+ | * [https://xkcd.com/399/ XKCD Cartoon on TSP] | ||

+ | * [https://www.youtube.com/watch?v=YX40hbAHx3s P vs NP] | ||

+ | ==== Braiding + Card Weaving ==== | ||

+ | * [https://www.cs.arizona.edu/patterns/weaving/topic_braiding.html Braiding] in Griswold's Weaving Archive | ||

+ | * [https://www.cs.arizona.edu/patterns/weaving/topic_tabletweaving.html Tablet Weaving] in Griswold's Weaving Archive | ||

+ | ==== Braiding Techniques ==== | ||

+ | * [https://loopbraider.com/ Loop Braiding] | ||

+ | * [https://www.schleich-s.com/en/US/horses/braiding-techniques/ Braiding Techniques] for horses | ||

+ | ==== Braiding Tools ==== | ||

+ | * [http://craftdesignonline.com/ Online Braiding Tools] | ||

+ | * [http://www.jbead.ch/ Bead Crochet] Software | ||

+ | * [http://www.guntram.co.za/tabletweaving/gtt.htm Guntram's Tablet Weaving Thingie] | ||

+ | * [https://archive.org/details/AtariComputerDesignBandWeaving ATARI band weaving] book + disk | ||

+ | ==== Rope Weaving ==== | ||

+ | * [https://www.youtube.com/watch?v=uX9DJp_pfgM How to weave a Rope Mat] | ||

+ | * [https://www.youtube.com/watch?v=_VdOId9jmN8 Rope Weaving Clinic] | ||

+ | === Books === | ||

+ | * Y. Kyosev, ''Braiding Technology for Textiles'', ISBN 978-0857091352 + [http://www.sciencedirect.com/science/book/9780857091352 ebook version] | ||

+ | == Nets == | ||

+ | In this class we had a look at graphs and networks, both in the textile and the social domain. | ||

+ | === Network Analysis === | ||

+ | We had a look at knotted networks and discussed possible representations | ||

+ | * We discussed which properties of the textile net are important, and which properties can be abstracted away | ||

+ | * We looked at different ways of creating a network from single pieces of thread or a single continuous piece of thread | ||

+ | * We found that a graph representation may not be a suitable model for textile networks | ||

+ | ** If we care about the network structure, nodes of degree two (a node with two edges) may not be meaningful | ||

+ | ** However nodes of degree two could serve to represent a knots in a single thread | ||

+ | ** We could encode the distance between knots (weight of an edge) | ||

+ | ** If we follow a thread through the network, direction might play a role as well (directed edges) | ||

+ | === Network Construction === | ||

+ | We wondered how networks can be constructed from a single thread. | ||

+ | * We found that some networks can't possibly be constructed from a single thread | ||

+ | * We had a look at the Seven Bridges of Königsberg, and tried to figure out which conditions need to be met, to find a path that crosses all bridges exactly once (Eulerian path) | ||

+ | * We found there is a complementary graph for people who use a boat and try to cross under all bridges exactly once | ||

+ | * We learned about the classic problems of graph theory | ||

+ | ** Visiting each places / node exactly once in a single tour (Hamiltonian Path) | ||

+ | ** visiting each bridge / edge exactly once in a single tour (Eulerian Path) | ||

+ | ** The Travelling Salesman Problem (TSP) | ||

+ | === Regular Networks === | ||

+ | We explored various tilings, and the networks that result from their edges. | ||

+ | * We had a look at regular tilings of the plane, and the node degrees of the resulting networks | ||

+ | * We discussed which of the tilings can be turned into networks using a single continuous thread and how to do it | ||

+ | * We had a look at pentagonal tilings of the plane, and the kind of networks that they would yield | ||

+ | === Random Networks === | ||

+ | * We discussed how we can create networks in a random but controlled manner | ||

+ | ** Using a dice to randomly decide which knots to connect | ||

+ | ** Modify knotting probability based on the degree of a knot | ||

+ | * We learned about the history of small world and scale free networks and their properties | ||

+ | === Network Topology === | ||

+ | * We learned about graph embeddings, and that some graphs cannot be embedded in the flat plane without edges crossing | ||

+ | * Accordingly some networks cannot be laid out without threads crossing | ||

+ | * Networks may be filled with inflatables to create interesting 3D shapes. (see also: Knitflatables) | ||

+ | === Homework === | ||

+ | * Find personal, autobiographic or social relations, that are important to you | ||

+ | * Can you represent those as a knotted network? | ||

+ | * Consider the use of knotted networks to store and communicate the flow of resources, family relations etc. | ||

+ | == Meetup == | ||

+ | We talked with Katrin Steiger to discuss the inclusion of our experiments in the upcoming future vintage exhibition. | ||

− | ... | + | === Links === |

− | == | + | ==== Travelling Salesman Problem ==== |

− | == Networks == | + | * [https://www.youtube.com/watch?v=-cLsEHP0qt0 Travelling Salesman Problem] with Thread |

+ | * [http://www.cgl.uwaterloo.ca/csk/projects/tsp/ TSP-Art] | ||

+ | * [http://blog.ninapaley.com/2013/08/30/the-traveling-horse-salesman/ TSP-Animation] | ||

+ | ==== Paths in Graphs ==== | ||

+ | * [[wikipedia:Eulerian_path|Eulerian Path]] | ||

+ | * [[wikipedia:Hamiltonian_path|Hamiltonian Path]] | ||

+ | ==== Sorting Networks ==== | ||

+ | * [https://www.youtube.com/watch?v=LOxfdsBBjKI CS-Unplugged] | ||

+ | * [[wikipedia:Sorting_network|Sorting Network]] | ||

+ | ==== Tilings ==== | ||

+ | * [[wikipedia:Euclidean_tilings_by_convex_regular_polygons|Tilings by Convex Regular Polygons]] | ||

+ | * [[wikipedia:Penrose_tiling|Penrose Tiling]] | ||

+ | ==== Knitflatables ==== | ||

+ | * [https://issuu.com/yuliya_baranovskaya/docs/knitflatables_ybaranovskaya_2310201 Knitflatable Architecture] | ||

+ | ==== Random Networks ==== | ||

+ | * [[wikipedia:Random_graph|Random Graph]] | ||

+ | * [[wikipedia:Scale-free_network|Scale-free network]] | ||

+ | * [[wikipedia:Small-world_network|Small-world network]] | ||

+ | * [[wikipedia:Boolean_network|Boolean Network]] |

We explored what kind of geometric constructions we can do with thread, chalk and the help of several people...

- how to draw a line
- how to draw a circle ( d = const.)
- how to draw an ellipse ( a + b = const.)
- how to draw multifocal ellipses (a + b + c = const.)
- how to draw egg-shaped curves (3 * a + b = const.)
- how to measure the circumference of a circle
- how to calcualte pi using only thread (See also here)

We explored how our thread-based drawing tools could be used to identify points on the surface of shapes in 3 dimensions.

- We discovered the 3d ellipsoid (a + b = const.)
- We found that multifocal 3d ellipsoids have a doughnut-topology.
- We found two different ways to create ellipsoid shapes:
- the polygon method, where the thread forms a polygon going through the focal points and the drawing point
- the star method where the thread is alternately visiting each focal point and the drawing point

- Geometric knowledge from school only got us so far ...
- There is a whole universe of "new" shapes and forms

- Questions regarding surface of different shapes popped up
- We discussed different methods of measuring the surfaces using thread

- What could an Experimentier-Baukasten / a kit / a sandbox for computing with thread look like?

Do some research on other kinds of kits! - Do some thread-based geometry at home. Pick a parameter such as the thread-length and vary it systematically
- Document your thread-art in the wiki

Some links to classics of compass + straightedge geometry

as well as the thread-based geometry we explored in our class.

- Tim Ingold:
*Lines: a brief history*, ISBN 978-0415424271 (hint: google it) - Kandisky:
*Punkt und Linie zu Fläche*

- Ellipse on Wikipedia
- Multifocal oval curves on Wikipedia
- On the description of oval curves by James Clerk Maxwell
- Semidefinite Representation of the k-Ellipse

- Compass and straightedge construction on Wikipedia
- Byrne's version of Euclid's elements using coloured shapes (very bauhaus)
- 3D Sculptures by Helen Friel

Here are some links to all kinds of kits.

May they serve as inspiration for creating your own textile computing kits.

- Anker-Steinbaukasten
- LECTRON Elektrobaukasten
- LEGO, KNEX, LEGO-Mindstorms ...

- Sewing Box with Implements
- Sewing Box Cabinet by Kiki van Eijk

- Survival Kit
- Dentist Toolkit
- Pictures of surgical sets and tool boxes

- The Charkha (spinning)
- Hexagonal Weaving loom (hexagonal weaving)
- Tablet Weaving (weaving/braiding)
- How to make a Kumihimo Disk out of a CD (braiding)

- various knot books online and offline
- We learned how ropes are made in a "Seilerei" on the "Reeperbahn"
- We learned about a rope inspection machine, that travels along a the cable of a "Seilbahn"

- We learned the basics of knot theory
- Minimum number of crossings
- Knot-Invariants and Knot-Polynomials

We played a knot identification game.

It goes like this:

- Student A creates two knots using thread.
- Student B tries to figure out whether or not the two knots are the same

Create a nice framework for displaying knots.

The framework can be physical, graphical or computational in nature

- Teslaphoresis (self-assembly of threads)
- Spontaneous Patterns in vibrated Ball Chains: Knots and Spirals

- History and Science of Knots
- Animated Online Encyclopedia of Knots
- Encylopedia of Knots and Fancy Rope Work ISBN 978-0870330216

- Gordian Knot (mythology)
- Harry Houdini (magician)
- Abbot's encylopedia of rope tricks for Magicians ISBN 978-0486232065
- Self-Working Rope Magic: 70 Foolproof Tricks ISBN 978-0486265414
- Seil-Salabim

- Splicing Animated.

- Knot Theory Videos by Numberphile
- How Mathematics gets into Knots
- Alexei Sossinsky,
*Mathematik der Knoten: Wie eine Theorie entsteht*, ISBN 978-3499609305 - The Knot Atlas
- Historic Knot Tables

- Hojōjutsu japanese martial arts technique
- Shibari arte documentary on japanese bondage
- Go get knotted a blog to learn bondage knots
- Enchanted Forest photo series by Garth Knight

- Manipulation of Deformable Linear Objects feat. Un-Knotting Bot
- Knotting/Unknotting: Manipulation of Deformable Linear Objects

In this class we identified the basic elements of braids, and explored the intersection of braiding and sorting algorithms.

- We developed and discussed different notations for braiding
- We played a game involving three persons
- The first person creates a braid
- The second person describes the structure or construction of the braid using words only
- The third person recreates the braids accordingly

- There are different ways to describe the structure of a braid
- structure vs construction
- position-based vs thread-based

- Some instructions will not result in a braid
- Some systems are simpler than others, but may not be universal in the sense that they can describe every possible braid

- We discussed why sorting is an important topic in computer science
- We got to know the concept of computational complexity and the big-o notation
- We re-enacted several sorting algorithms using threads and chalk
- We developed collaborative sorting algorithms resulting in braids

- Bubblesort is a fun collaborative activity
- The mapping from sorting operations to operations of textile construction is important
- If the mapping is bad the result may not be a stable (overs and unders)
- If the mapping is bad the result may not be dense (no-ops vs crossings)
- Sorting networks allow for parallel sorting / braiding

- French Children's book feat. Maypole Dance + Track Diagram
- Pet Flakes Architecture inspired by Maypole braiding
- Bobbin Dance by Shane Waltener

- Sorting Networks by Computer Science Unplugged
- Bubble Sort as hungarian folk dance
- Bubble Sort
- Merge Sort
- Insertion Sort
- Quick Sort

- Braiding in Griswold's Weaving Archive
- Tablet Weaving in Griswold's Weaving Archive

- Loop Braiding
- Braiding Techniques for horses

- Online Braiding Tools
- Bead Crochet Software
- Guntram's Tablet Weaving Thingie
- ATARI band weaving book + disk

- Y. Kyosev,
*Braiding Technology for Textiles*, ISBN 978-0857091352 + ebook version

In this class we had a look at graphs and networks, both in the textile and the social domain.

We had a look at knotted networks and discussed possible representations

- We discussed which properties of the textile net are important, and which properties can be abstracted away
- We looked at different ways of creating a network from single pieces of thread or a single continuous piece of thread
- We found that a graph representation may not be a suitable model for textile networks
- If we care about the network structure, nodes of degree two (a node with two edges) may not be meaningful
- However nodes of degree two could serve to represent a knots in a single thread
- We could encode the distance between knots (weight of an edge)
- If we follow a thread through the network, direction might play a role as well (directed edges)

We wondered how networks can be constructed from a single thread.

- We found that some networks can't possibly be constructed from a single thread
- We had a look at the Seven Bridges of Königsberg, and tried to figure out which conditions need to be met, to find a path that crosses all bridges exactly once (Eulerian path)
- We found there is a complementary graph for people who use a boat and try to cross under all bridges exactly once
- We learned about the classic problems of graph theory
- Visiting each places / node exactly once in a single tour (Hamiltonian Path)
- visiting each bridge / edge exactly once in a single tour (Eulerian Path)
- The Travelling Salesman Problem (TSP)

We explored various tilings, and the networks that result from their edges.

- We had a look at regular tilings of the plane, and the node degrees of the resulting networks
- We discussed which of the tilings can be turned into networks using a single continuous thread and how to do it
- We had a look at pentagonal tilings of the plane, and the kind of networks that they would yield

- We discussed how we can create networks in a random but controlled manner
- Using a dice to randomly decide which knots to connect
- Modify knotting probability based on the degree of a knot

- We learned about the history of small world and scale free networks and their properties

- We learned about graph embeddings, and that some graphs cannot be embedded in the flat plane without edges crossing
- Accordingly some networks cannot be laid out without threads crossing
- Networks may be filled with inflatables to create interesting 3D shapes. (see also: Knitflatables)

- Find personal, autobiographic or social relations, that are important to you
- Can you represent those as a knotted network?
- Consider the use of knotted networks to store and communicate the flow of resources, family relations etc.

We talked with Katrin Steiger to discuss the inclusion of our experiments in the upcoming future vintage exhibition.

- Travelling Salesman Problem with Thread
- TSP-Art
- TSP-Animation