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On the day I visited the Science Museum to hand over Square Deal, Counting Pane and Pythagoras Tree, the Curator of Mathematics, Jane Wess asked, ‘Can you knit a Peano Curve?’ I had no idea as I had never heard of a Peano Curve. She said she would let us have some information and a few days later we received a letter containing some pages photocopied from an academic tome. We studied it but decided it could not be done.

We learned that a Peano Curve is a space filling curve and is rather like a fractal. It follows a simple path round a square but each section of it can be split up to reproduce that path on a smaller scale. Theoretically this happens again and again until the whole surface is completely covered. We couldn’t knit it but we kept the paperwork.

About two years later, on our way home from a maths conference, we went to visit
Alec Dalglish of the Knitting Craft Group who we had been communicating with him
for some time. He was retiring and would have liked us to take over the running of
the organisation. It wasn’t for us. We knew it wasn’t the way we wanted to go but,
as our journey home from the conference took us close to where he was, we agreed
to visit him. We spent a delightful afternoon in his office. He produced interesting
box after interesting box and it was all very tempting. He had several items created
by well-

Steve knew something was going on in my head. He’d seen me go off at a tangent often
enough before. This was more than a tangent. It was time to abandon all our self-

A Peano curve is a complex thing. It twists and turns and packs itself together so that, theoretically, it fills all the space on a surface. The computer, and son Ben, came to the rescue again. Ben has the ability to assimilate information more quickly than either of us and in the time we were thinking about how best to draw it he had drawn five or six generations of the curve showing how it packs itself together. To turn this curve into something we could hang on the wall needed a bit of thought and we eventually decided it had to be in two parts. First it needed a grid to represent the graph paper or squared paper it would normally be drawn on. The curve itself could then sit on top of this.

I am not a very experienced crocheter but this would only require basic skills. The first problem was how to get perfect squares in the grid, with the spacing needed. I made several attempts and then thought of a way to avoid some of the trial and error. By the magic of email I had a reply from James Walters within the hour. James is an expert crocheter, with a thorough understanding of the maths needed, and he had the information at his finger tips.

I made the grid, in black, with perfect squares. The curve was in the brightest shade
of green I could find. The technical part of the crocheting was simple. It was just
a chain attached to the grid at strategic points. The demanding part was keeping
track of those strategic points. Originally I was trying to work from a single sheet
of paper showing the entire curve. When it is finished it is clear that the curve
forms little blocks, and lines can be seen criss-

Just after it was finished we allowed ourselves to be talked into going to a Maths
and Art weekend at Oxford University. We didn’t want to go. We were sure we would
be out of our depth. We didn’t know enough about maths or art to mix with such august
company. Against our better judgement, John Sharp talked us into it and asked us
to bring the newly-

This first crochet hanging was named Peano Beano. Elements of doubt began to creep
in when John whispered that the name was actually pronounced ‘pee-

When we got home, with the magic of the now rapidly expanding Internet, it didn’t take long to discover the truth. They were all correct! What we had represented was a Hilbert Open Peano Curve. We also found that there was a Sierpinski Closed Peano Curve so, naturally, we made that too.

It seemed sensible to drop all mathematical references from their titles. The first became Spacecraft, the other became Square Snowflake.

The idea of space-

SPACECRAFT