the maths of miyake

Yes, here is yet another Issey Miyake maths inspired collection!

I was really excited to learn of Miyake's Autumn/ Winter 2010/11 ready to wear collection, a collaboration between Issey Miyake's creative director Dai Fujiwara and William Thurston, Professor of mathematics and computer science at Cornell University. "We used the technology of mathematics to make art" said Fujiwara at the opening show in Paris this March.

Fujiwara and Thurston share an interest and enthusiasm in three dimensional design, so the  collection entitled '8 Geometry Link Models as a Metaphor of the Universe', based on the fundamental geometries of three dimensional spaces, was of mutually beneficial interest to the pair. This article from ABC news and this interview on You Tube by Parismodesen gives an interesting insight into the common interest that unites these two seemingly disparate professions. Thurston explained "We are both trying to grasp the world in three dimensions, under the surface, we struggle with the same issue."

Fujiwara created garments based on different elements of Thurston's principles, resulting in inwardly twisting, knotting and crossed draped fabrics.

These designs have been criticised for there over simplified form, and there is no doubt that they are only loosely based on mathematical principle and not a literal interpretation, but then they have been used as inspiration, rather than to communicate an idea.

As one of my main focuses for this research I am looking at the question can maths be beautiful? As a designer I find these interpretations of mathematical ideas aesthetically pleasing. Is that because beauty truly lies 'in the eye of the beholder', or is there actually a winning formula that the majority of us would agree as beautiful? I find this collection of particular interest as there are many similar mathematically knitted objects already out there on  websites, such as that of Sarah - Marie's: The Home of Mathematical Knitting.

Even if the 'perfect' pattern is defined for us by the laws of mathematical 'beauty' (that of proportion & symmetry etc), there will always be a very personal design decision made by the knitter as to choice of scale, tension, yarns and colour used, and it appears to me that it is these elements that determine as much aesthetic value as the pattern itself.

the science of knitting

Today I have been concentrating my research on the relationships between maths, science & knitting. There are more links out there than you might initially think.

The name that crops up most when researching this category is that of Daina Taimina, a mathematician who teaches at Cornell University in New York. She made a significant scientific breakthrough by inventing what is now known as 'hyperbolic crochet'. By using a handicraft technique she produced a surface model of a hyperbolic plane, something that until that time had only been understood as an abstract concept. This article in The Times explains it much better than I ever could!

Hyperbolic crochet

The fashion & knitwear designer Sandy Black has a different link with the subject. She studied pure and applied mathematics at University College London, where she also bought her first knitting machine and began to combine her two favourite subject matters together.

This article demonstrates Black's theories linking maths and knitting.

Sandy Black is now Professor of Fashion and Textile Design & Technology at the London College of Fashion University of the Arts London. She is also Director of the Centre for Fashion Science, an institute focusing on research into:

• Considerate design
• Direct 3D design and manufacture
• Digital Studio: Direct 3D design and manufacture/ blending the real and the virtual
• Seamfree production in knitting, welding and rapid prototyping technologies
• Mass customisation for fashion and footwear
• Multifunctional textiles and fashion
• Living Colour
• Cosmetic Science

There is some fascinating sustainable designing going on here. Check out the Wonderland projects dissolvable dresses! The idea behind this is to develop a plastic that usefully degrades once it's use has expired. In this instance the dress dissolves into a gel that can be used to grow plants.

The subject of architectural knit is also pretty exciting. There seems to be a surge of development towards knitted performance fabrics. CITA, the Centre for Information Technology & Architecture in Denmark has developed some fantastic 'working' textiles such as this blend of Kevlar, polyeurethane and carbon fibre which has been knitted into a composite material for building structures.

Another collaborative project undertaken by this company is that of CNC knitting and CAD Architectural software, resulting in the design of Listener, a smart material that reacts, via sensors woven into the construction of the fabric, to the human touch.

I came across the above two developments from a blog called Fashioning Technology by Syuzi Pakhchyan. It contains posts that explain how to combine craft & technology to make electronic working and wearable art pieces.

Along similar lines, I came across this article in Knitting Industry News, which showcased the development of the Cullus fabric which has sound absorbent properties.

Cullus is a flat knitted material. It can be hung as flat panels or manipulated into three dimensional objects. It is interesting to observe that the sound absorbency qualities are the same, regardless of the form taken by the material.

As well as these very technical, industry developed fabrics, there is also a lot of interest in science and maths related knitting going on in the domestic circle.

When searching on Wikepedia the link to Mathematics and fiber arts brings up many sites where ordinary people have knitted objects based on mathematical or scientific theory.

A good example of this would be the DNA scarf, commissioned by Dr. Thomas Montville a Professor at Rutgers University, New Jersey from one of his students, June Oshiro.

This article has an interview with Oshiro, now a microbiologist in Food Science, describing how she was inspired to describe a double helix in yarn whilst persuing her PhD research.

I have found many other objects of interest created by domestic knitters to illustrate or answer some of these mathematical questions. This website has some interesting patterns and ideas, from the klein bottle hat to the Fibbonacci sleeveless shirt, but from a design perspective, most lack aesthetics.

Overall, it would appear that there is a definate interest from scientists about the value of craft techniques, especially knitting & crochet, and a reciprocal interest from artisans to collaborate on projects.

I came across a blog by Andrew Maynard, Director of the Risk Science Center at the University of Michegan School of Public Health. It's called 2020 Science and one post in particular, knitting science,  discusses why there is this growing interest between knitting, science and mathematics.

"Knitting patterns as code for complex three dimensional structures - it's an idea that makes perfect sense when you think about it. After all, DNA uses sequences of four molecules to code for complex protein structures, so why not use deceptively simple "knit one purl one"- type sequences to construct complex shapes."

This blog has many relevant links to my subject and confirms to me that there are parallels between these areas that have begun to be explored by others, but I feel really excited that there is still plenty for me to investigate.

shima versus silvereed - the battle of the machines

I have been thinking a lot recently about which techniques and machinery I want to use in my creative project, and thought I'd better start writing it down in order to make some sense of it.

There seems to be so many possibilities that it baffles me deciding in which direction to go. The lack of decision on a final product ultimately makes it difficult to decide what equipment to use.

At Uni we have domestic Silvereed knitting machines and Dubied Industrial machines. There is of course, the option of finding someone to lend me their Shima for a few days.....?

I have turned over the question of the Shima Seiki in my mind for some time now, and think that I have finally resolved my dilemma about the pros and cons of using one.

Having had the amazing oppurtunity of doing my BA at a University that gave me the experience of designing and processing work on this machinery, I feel that I can confidently say that this is not the correct route for me to go down with this MA, or most certainly not at this stage and time.
There are several reasons for this. Firstly, one of my main aims for doing my Masters is to develop a working practice/ sustainable business from whatever product I develop. Using a Shima is neither physically or financially practical for me. Having spoken to the Director of Textile Studies at my old University, and a Senior knit lecturer at Kingston the practicalities of designing and using a machine at another university are limiting.
I made enquiries at Shima Seiki UK about the possibility of owning the software programme, designing at home and then 'bureauing' out to a company to knit the designs, as there is in other textile disciplines. I was told that the software is not sold seperate to the machinery and if it was would cost about £26,000! So that answers that question! Also, as brilliant as this equipment is, it does not lend itself well to several of the techniques that I am keen to take forward...for example, the knitted pockets are achievable on the Shima, but it is an impossibility to stop the machine and open the bed in order to place things inside, as I have done on the Dubied.

So on to the Dubied. I have a love hate relationship with these machines. These days it is more love than hate as I have become more confident and familiar with their sensitive quirks! I definately want to make use of these machines as they can achieve beautiful quality knits, and work both finer and chunkier than the domestic machines available. They have a double needlebed which allows me to work on just the front, or just the back of the knitting and to close the beds and knit across both, allowing greater versatility in my work. However, they don't allow me to hold stitches easily, which is something I really need to be able to do in order to create 3D effects.

After completing Year 1 of my degree course at the University of Derby, progressing to working on a Dubied in Year 2 and then onto using the Shima in my third year, I had dismissed the idea of ever working on a domestic knitting machine ever again. That was until I visited Knit-1 in August, and whilst there brushing up my skills on an industrial machine knitting course, I was wowed by the work that was being produced on the humble domestic machine. I think I had been put off by all my first year dropped stitches and clumsy attempts at fairisle using horrid coloured acrylic yarn that I never pushed the boundaries beyond the 1980's home knit conotations and realised the full potential of the machine.

Ironically enough most of my research and experimentation into constructing three dimensional knitted fabrics begins with partial knitting or short rowing, a technique most easily achieved on the domestic machine through the use of the Russell levers /Holding button. This allows me to hold some of the stitches, whilst knitting on others, exactly as you would in hand knitting when stitches would be held by moving them to a seperate needle or stitch holder.

The other advantage to the domestic machine is that you can add the ribber attachment to create a doublebed machine. This is not quite as smooth as the dubied, but something that opens up possibilities of having two needlebeds and the holding button on one machine.

The other technique I am interested in experimenting with is turning the knitting on the machine. When you knit on a machine there is garter stitch one side and stocking stitch the other. By the use of a garter bar you can pull all the stitches off the machine, turn them around and (hopefully!) put the knitting back onto the correct needles to resume knitting. Therefore creating stripes of alternate stitches.
I found this brilliantly innovative site which shows me how to make my own garter bar out of a metre rule and some hair clips....watch this space for the results.

science museum(s)

As inpiration for my research topic I visited both the History of Science Museum in Oxford, and the London Science Musuem. I only had a short amount of time in each, and took hundreds of photos to make up for this. Another visit is definately due.

In particular I liked the 'Strange Surfaces' exhibition in the Mathematics section of the Science Museum. This included mathematical surface models made of cardboard and string. These are an example of descriptive geometry and have been used to illustrate geometric ideas in mathematics since the 1840's.

'A mathematical surface model is one that follows a mathematical formula or definition, or illustrates a mathematical concept'.

In particular I liked these cardboard sliceforms by John Sharp. They made me think of different ways of cutting and joining and contructing shapes. I suppose there are lots of possibilities in the area of three dimensional knit design to cover and wrap a supporting framework in knitting. This is an area I have thought about before and rejected. Part of my interest in this area is in developing and manipulating the fabric on the machine and not afterwards. It has reaffirmed the idea that I definately want to construct from within the fabric, and then construct a product from that fabric.

The mathematical instruments were inspiration in themselves.

Everything about these instruments is pleasing to me. The symmetry, repetitive patterning and grid divisions as design inspiration. Also, something about the similarity to the knitting machine bed makes me think of patterning & counting as I work.

A sketchbook sample based on these ideas

Once again the use of glass and light in the form of prisms and telescopes (and this cylindroid) had me thinking of relection and refraction.

As you would expect there were also hundreds of other brilliant and inspiring three dimensional objects on display. Here are a few more:

All of these shapes and colours and structures have energised my 3D aspirations, and given me a bit of clarity of how I am going to combine my inspirational science & maths subject matter with knitting.

london design week

In September I visited Tent London & 100% Design as part of London Design Week. My aims were to gauge the target market for 3D textile design (particularly knit), check out the competition and gain inspiration & direction for my Masters creative project.


Not holding out much hope on the knitting front I was amazed that the first thing that greeted me at the Truman Brewery entrance into Tent was the 'Giant Knitting Nancy' by Superblue Design.

More of a community project than a piece of textile art, this giant 3D structure combines creative participation with a growing seating and play area. Still food for thought on a grand scale for 3D knit design.


There were some amazing interiors products on display at both trade shows, but probably the two I felt were most relevant to me were that of Penelope Jordan (Tent) and Siwen Huang (100% Design).


Penelope Jordan creates textile art pieces. Her work combines colour, structure and three dimensional design through placing and folding "a variety of textiles in a controlled repetitive order".

Although my work has a very different aesthetic from Penelope Jordan's, I feel there is a similarity in both the ethos and the outcome. She too is interested in traditional craft skills and the making process, but brings a contemporary twist through her designs and use of materials.


Siwen Huang is a textile designer with a range fabrics that she describes as 'textile futures'. She specialises in collecting and redirecting light for pattern creation.


"I used reflective and flexible materials to create three dimensional optical surfaces, by laser cutting and hand finishing techniques. The finished pieces distort and redirect light as it hits the surface creating illusory and ambiguous surfaces."

It seems as though there is a very clear pattern emerging within the designers and exhibitions I am inspired by.  That of combining traditional and modern textile techniques, the repetitive order of designs and the creative use of light and shadow to form part of the design.


As far as my aims to gauge the target market went, it appears that there is a lot of interest in creating three dimensional textural surfaces, everything from fabrics to wallpapers to textile art. 
There were industrially knitted performance fabrics on show at 100% Design,  but no three dimensional innovative knitted fabrics for either fashion or interiors.

blanka sperkova

Blanka Sperkova is a jewellery designer who is probably best known for her organic wire sculptures.

She has perfected her unique way of working, a form of finger knitting inspired by traditional wire and lace making techniques from her Slovakian homeland.

Whilst neither a fashion designer nor a machine knitter, I came across Sperkova's sculptures in my search for three dimensional knits, and was fascinated by the degree of freedom of manipulation her chosen media allows. I am still uncertain in which direction my work is going...fashion or interiors? It is helpful to see this designers work and contemplate this.

She creates internal forms, experimenting with lighting and film to animate the sculptures, so that the shadows cast become more expressive than the original object.

"My objects take shape from within themselves; they anticipate themselves. There is matter, then form. Or there is form, then matter."

The use of light and shadow fits well with the latter two pieces of work shown on my first blog. I have used laser cut coloured acetate to form a pattern, but it only really works when it is backlit, then a whole new dimension is added.

Sperkova's designs led me to look further into knitting with wire, and specifically machine knitting with wire. I consulted 'Textile Techniques in Metal' by Arline Fisch.

It would appear that the biggest problem when knitting wire on a knitting machine is tension control. It is also advisable to cast on in yarn to begin with, then knit 1 row with yarn & metal together, before dropping the yarn and knitting solely with wire.

Materials that knit well are: fine silver wire, fine brass wire and copper insulation & electrical wire.

Tubular knitting with a knitting dolly or sock machine also appears to be a successful pursuit.

liz collins

Liz Collins is an American designer and artist who combines machine knitting with techniques of fabric manipulation to create wearable art pieces.

Whilst studying for her degree she came across the idea of 'knit grafting', a technique of hanging fabric from the latch needles during the process of machine knitting. This technique has allowed her to layer and fuse varying fabrics into her designs, creating sculptural forms over a tightly knitted bodice.

"It was a form of alchemy - turning simple cones of yarn into three dimensional, multilayered, and wearable pieces in a very short time frame."

The idea of constructing a multilayered and multi textured fabric is an interesting one. Like Sandra Backlund, Collins also says that the fabric itself is of 'perpetual ongoing inspiration' to her.

I like the way that Collins manipulates form whilst the knitting is still on the machine, building the garment and the fabric simultaneously.

One of my points of research is to look at the different ways in which I could construct shapes, other than by altering the surface of the fabric. I am interested in the way seams could be joined and moved to alter form, creating shapes from a single piece of fabric and examining contouring, shaping and placement within this theme. The technique of 'fabric grafting' is not unknown to me, and is a definite point of interest when thinking of alternative ways to join seams.

Collins is also known for working with experimental materials, something else I am keen to research on this MA. She is quite strategic in her methods, taking advantage of the natural stretch in the knitting, working with complimentary and contrasting fabrics to create shape, volume and silhouette.

Looking at this designers work has made me think a lot about the types of yarns I am using, and the possibilities and differences I could create within a technique by using high or low twist yarns, or by using a combination of natural and manmade fibres to experiment with shrinkage or expansion in the natural elements when heated or washed.

sandra backlund

Sandra Backlund is a Swedish fashion designer best known for her chunky architectural knitwear. She has to be one of the most recognised and exciting contemporary knitwear designers in Europe.

Her innovative designs are pieced together from individually crafted elements that evolve into three dimensional formations.

These designs are constructed textiles at its extreme. They verge on the borders of wearable art, and are certainly created through a process more affiliated with sulpture than fashion design.

She says about her designs:

"My work is very personal to me. I improvise and allow myself to loose control and see what happens if I do not think so much about practical things. The human body is always the starting point. I am really fascinated by all the ways you can highlight, distort and transform the natural silhouette with clothes and accessories."

Backlund's designs fascinate me, and as inspiration for my proposed creative project, they certainly give me a lot to contemplate concerning design & construction. I feel the urge to unpick and unravel,  to deconstruct and dissect.

Her work is quite different to my intended outcomes as she uses mainly hand knit and crochet techniques, working in heavy yarns as opposed to my finer machine knitted samples.

Mostly I am in awe of her concept. In a recent interview with Blend magazine she explains how her work is never planned, and how important the act of improvisation through coincidence and accident is in the evolution of her designs.

This is certainly an ethos I would like to aspire to. I think the process of knit naturally lends itself to this way of working as a fabric is created from scratch. I recognise that often losing count or forgetting to change colour can result in a more interesting effect than the one that was originally being strived for.

e-diary

I am a student studying at Bath Spa University for an MA Design: Textiles. This blog will show the online development of my research and progression of my creative work throughout the course. I am a knitter, and am fascinated by constructed and constructing textiles.

My aim is to create an aesthetically pleasing design based on three dimensional mathematical principles. I have always felt that writing a knitting pattern is akin to writing a formula that allows me to calculate a unique equation, or in this case, creation. Can knitting be scientific? Can maths be beautiful? By blurring the lines between the 'domestic' and the 'academic' I intend to create a formula that satisfies everyone, communicating unfamiliar ideas through accessible design.

Here are some recent samples I have been working on: