A Stitch in Hyperbolic Space

I find the hybrid materiality aspect of this course fascinating, even if it was a little hard to get my head around at first. I was really interested combining both traditional and modern techniques and experimenting with their outcomes.

I knew I wanted to experiment with crochet as it is one of my most favoured crafts, but also because it is one of the only traditional handicrafts that remains unmechanised due to the complexity of its stitches. I love the juxtaposition between this craft in particular and digital fabrication.

I originally wanted to work with cork as I love how versatile material it is, but it ended up just crumbling and the more reinforced cork I could get was unsuitable for laser cutting so I decided to experiment instead with 3D printing and laser cut MDF & acrylic.

I began working with the 3D printed shapes, experimenting with winding and slipping the yarn round the shapes but the fastening was never secure so I settled with attaching the yarn to itself surrounding the shape with a slip stitch and a single crochet.

For the purposes of clarity, I refer to crochet in the American terminology as I feel it is the more clear naming system. British terminology refers to the number of loops pulled through on the hook to create the stitch; whereas US terminology refers to the number of loops on the hook at the beginning of the stitch. So US single crochet (SC) it is the equivalent of the UK double crochet (DC), US double crochet (DC) is the equivalent of UK triple crochet (TC) and so on.

I first began with this shape, placing single crochet stitches on the 3D printed frame and moving around the shape. Then I wound yarn in and around the posts. I found it quite interesting. It reminded me of an old style coffee table my gran used to have. Minus the looped yarn round the legs of course.

I continued with my exploration of the 3D shapes with the single ring. I again attached the yarn with a slip stitch and enclosed it completely in single crochet stitches. I continued in a round with this shape rather than slip stitching the end of the row to the beginning and then beginning a new row. Instead, I continued in a round without stopping, drawing the shape outward to create a bowl-like shape. I liked this as it was quite similar to the way a 3D printer creates a shape.

The 3rd 3D printed shape I created with very small sections so used a thread to crochet in and around the form which, as I crocheted I thought it looked like the centre of a flower so decided to crochet single, double and triple crochet stitches to form petals and created a 2nd layer of petal like shapes in front with double crochet. Due to the fine nature of the thread, the finished experiment was not as effective as I would have liked.

After experimenting with the 3D printed forms, I began playing with the laser cut shapes. Again I found attachment of the yarn needed to be around the object in order to properly secure it. For each shape I stitched around the form, trying variations of stitches to create differing shapes shown below including single crochet, half double crochet, double crochet, treble crochet, double treble crochet and puff stitch (five double crochet stitches in the same stitch and closed together with a slip stitch.

I preferred the look and feel of the laser cut MDF in conjunction with the crochet yarn to the acrylic, however it was brittle by nature of the thickness, and by laser cutting the thin material it weakened it further; causing some parts to snap. The laser cut acrylic was much more sturdy and supportive throughout my experiments so I experimented further with the acrylic pieces than I did with the MDF ones.

No matter which material I used, it always gave me a solid structure to stitch around and added a secure base to the crochet which would have otherwise been limp even when done in the tightest stitches.

One of the most interesting experiments was when I decided to create an elongated tube off acrylic stars, I chose to use a smaller star in the centre and used single crochet to keep the resulting fabric tight together. I especially liked the way the shape of the fabric changed when the stars were twisted. It’s a lovely piece to look at.

During my explorations I became fascinated by the work of Christine and Margaret Wertheim who created the crochet coral reef. Unfortunately I cannot link any of their images without paying a fair usage fee however their work can be viewed here.

Their work concerns a response to global warming and the bleaching of the coral reefs using crochet to form hyperbolic space. Hyperbolic space is commonly seen in coral, sea slugs, lettuce, the way the brain is formed and other such natural occurrences. For centuries mathematicians have struggled to recreate the shape until in a project in 1997, Dr Diana Taimina discovered how to recreate this geometry in the medium of crochet.

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=2ahUKEwjfxea056blAhVIzhoKHVFbDf0QjRx6BAgBEAQ&url=https%3A%2F%2Faeon.co%2Fessays%2Ftheres-more-maths-in-slugs-and-corals-than-we-can-think-of&psig=AOvVaw2eXgyWsoQdLecnPazow6bZ&ust=1571522415781369

The Wertheim twins took this discovery and used it to create the organic shapes of coral in yarn. I was deeply inspired by the work of the two sisters and it prompted me to finish my work in this flavour using the hyperbolic space shape.

In this part of the final artefact I attached three of the experiments adding the hyperbolic space theme through curls running along the sides of the yellow triangle.

This main piece of the final artefact was created with one of the large acrylic circles stitching loops from chains and working in a round in the same way I created the blue ‘bowl’ I worked on this one completely freehand, with no plan and no uniform stitches. One of the things that the Wertheim sisters noted was that their mistakes, missed stitches and freehand work created more organic and real looking work and I carried that into this piece.