Interpenetrating layers/interleaving knitting

As most of you know, I work for National Museums Scotland, I mainly work in Information Management and look after the staff intranet, and therefore don’t have many dealings with the actual objects in the Collections.

However, I was chatting to Julie Orford, Assistant Curator – Science, and knowing I had an interest in knitting, she told there were a couple of knitting/wool related objects in the Science and Technology collections. This might seem unlikely, but actually knitting is quite a mathematical pursuit, and knitting pattern instructions are a similar style to computer code. There are many knitting groups and knitters online that focus on science related knitting: knitted microbes, knitted DNA, knitting using the Fibonacci sequence or Pi.

Julie showed me some photos of knitted scientific models, here and here, made by Alexander Crum Brown (1838-1922), an Edinburgh scientist in the Museums Collections (not currently on display). He used the process of making these models to explore how interpenetrating layers work together. Some of his work is in other museum and library collections. He also invented the first stick and ball molecular models using double-pointed knitting needles and balls of wool: one of these models is in the University of Edinburgh’s collections, and a pair of his needles are in the Science Museum:

Crum Brown Knitting Needles

Photo © The Board of Trustees of the Science Museum (Creative Commons License)

Julie and I have written articles for the National Museums Scotland blog on Crum Brown knitting: Julie’s article, my article.

The models are triple layer knitting with 3 colours; immediately, I was curious to work out how he had created them. I initially assumed I could use the double knitting technique, where the yarn swaps from one side of the knitting to the other to change colours, and just add an extra layer in. I decided to create a piece of knitting of the National Museums Scotland logo. I created a chart with the 3 layers and colours included, which looked pretty mind boggling!

Original chart

I cast on 3 colours as 3 layers of knitting on my needle, putting in stitch makers every 9 stitches, to help me keep track of the stitches:

Triple knitting attempt

This was fine for the first few rows before the colourwork kicked in. However, once I came to the colours changing it became very difficult to keep track of which stitch was on each layer, and what colour I was knitting on to which colour below. I concentrated and persevered, and then realised I was getting colour blips  disrupting the pattern because I was knitting garter stitch:

Colour blips

which is when I realised this was not the technique Crum Brown had used, as he did not have the colour blips.

I told Julie Brown of my problems, and she brought me the models to have a look at in detail. By looking between the layers, I could see that the strands of wool pulled between the stitches to reach each of the layers, and actually each layer was one colour, and the stitches were swapped around to change the position of them.

Crum Brown stitches

e.g. If you have 3 coloured layers, orange (front), green (middle) and teal (back), and you wanted to change the colour of the next stitch, you would swap the position of the stitches to a different layer, orange to middle, green to back, teal to front.

I also realised from looking closely at the stitches of the models that they are knitted into the back of the stitch, although they are knitted on a fairly loose tension gauge to allow the stitches to move between the layers. The wool used is roughly an Aran weight.

Using this technique, it was too difficult for me to work with all the stitches on two needles, so I decided to try with a pair of needles for each layer. I had 2 sets of double pointed needles in 2 different colours, so I used them, as an easy solution to needing 6 needles the same size, and as my swatch was fairly small so I didn’t need long needles.

Six needles

I also changed the chart. Working from one main chart showing one layer (Layer 1) so I could see when I needed to change colour, and had small charts of the other 2 layers (Layer 2 & Layer 3) so I knew which colour was required on each layer:

NMS Crum Brown knitting chart

Rather than knitting each stitch, then moving it to the required layer, I moved the working yarn ready for the next colour change and crossed the needles to knit from a different layer.

I discovered it was easy to accidentally wrap the working yarn from the middle layer around a stitch at the front or back as I changed colours, which would look like this, and disrupt the pattern:

Wrapped stitch

To prevent this, I always returned the working yarn to its correct position after a stitch, and knitted the stitches in a specific order.

This was the final result:

This is what it looks like in action:

I thought it would be good to share this technique as it was so unusual, and not a technique that a knitter would naturally develop. Here are instructions (PDF) to create this small swatch for yourself:


I created a set of rules to follow for each type of working position for a stitch, and I have provided videos and a photo tutorial to follow.

This technique has not been tested, and I would welcome knitters to try it, and email me with suggestions of any improvements to the technique or instructions. There is not a written set of instructions of the chart. This technique is not suitable for beginners, but great for adventurous and curious intermediate and advanced knitters.

I did not knit through the back of the knit stitch, like Crum Brown, as it is not my natural way of working the knit stitch, and I didn’t want to complicate my knitting further. I wonder how close I have come to the way Crum Brown created his models? If I am close, it’s quite a tricky technique for someone to create, and I’m very impressed at his knitting prowess. I hope you enjoy knitting like Alexander Crum Brown too.


  1. This is amazing. Thank you for sharing it. Did you consider using a cable needle to shift the stitches around? I haven’t tried to do this yet, so I can’t work out whether that is a silly question!

    1. Hi Dani, Not a silly question. After giving up on the attempt on one needle initially, I didn’t try it again, as my head just couldn’t cope with the change of colours, and reading from a complex chart. Might be worth a try again with the less complicated circle chart, I just think it may be tricky to work out exactly which layer you are working on, when you have rearranged the 3 stitches with the cable needle, and I don’t know how well it would work getting the working yarn to the right place without accidentally wrapping the other stitches. If you have a go, let me know how you get on.

  2. I am a bit mindblown by the pic of 3 pairs of needles in your hands, Ruth – so impressed that you managed to produce this tiny bit of perfect knitting from that complicated start! think I’ll stick to I pair of needles for the time being ….

    1. He was exploring the way the interpenetrating layers worked together. Here is a quote from a journal essay that investigates his models:
      “Most of Crum Brown’s models represent variations on the mathematical surfaces described in his 1885 paper ‘‘On a Case of Interlacing Surfaces’’ (hereafter ‘‘Surfaces’’). ‘‘Surfaces’’ can be viewed as a contribution to topology, a branch of mathematics then in its infancy, which Crum Brown would likely have known as ‘‘the science of situation,’’ the name often used in Britain at the time. Described in 1876 as the study of properties of an object that ‘‘exist irrespectively of the magnitude and even of the shape of its
      parts,’’ this science might seem naturally poised to find knitted models, with their flexible magnitudes and shapes, especially useful; yet historical examples of topological knitting are rare.

      Faced with a research paper and accompanying models, we might conclude that the models were simply visual aids; I argue instead that Crum Brown’s knitted models were pieces of research in their own right, expanding rather than merely illustrating the work presented in the paper. His work is interesting not only as a rare example of early topological knitting, but as an example of abstract research taking the form of a crafted material thing. In a discipline whose primary output today is knowledge in textual and symbolic form, it is illuminating to consider how a piece of fabric could have been a hard-won product of research.”
      Dunning, David E., What Are Models For? Alexander Crum Brown’s Knitted Mathematical Surfaces. The Mathematical Intelligencer, Vol. 37, No. 2. Springer, New York, 2015 DOI 10.1007/s00283-014-9480-2

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