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The World of Illusion Knitting

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PICKING UP THREADS

This was written in
2007
so is now very dated

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-completed hanging. We went. We took the hanging. I also took a cute cuddly teddy bear. Maybe I thought appearing to be really eccentric would be an advantage and besides he was a rather special bear. He was dressed in a Mobius scarf and waistcoat, both of which have strange properties as they have only one side, instead of an inside and outside as you would normally expect.

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-arno’, so the name made little sense. We had not had time to assimilate this information when it got worse. One of the professionals announced that it was a Hilbert Curve, not a Peano Curve. We hadn’t heard of a Hilbert Curve so we were in no position to justify our claim. Before we had chance to collect our thoughts, we were witnessing a full-scale argument. There were two very distinct camps; one lot favouring Hilbert, the other Peano. It no longer mattered what we thought. These so-called experts could not agree amongst themselves. What they did agree on was that it was a unique piece of work that had given them all food for thought.

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-filling curves was fascinating and was to resurface later. It also took me back to my sixth-form days in school. The school was only a few years old when I first went there and most rooms had traditional wooden desks and chairs. The sixth form block was built after the rest and, in addition to the chairs I have already mentioned, the rooms were equipped with the latest innovation – plastic laminate tables. These tables had a very pale squiggly pattern on them and I delighted in going over the pattern with a pencil. It was amazing how long it took to cover a very small area as the curves twisted backwards and forwards and were very tightly packed.  I hadn’t heard of space-filling curves then but I’m sure their complexity must have infiltrated my brain.

These set the scene for the future though there were other knitted afghans in the pipeline. Have It All Ways showed all the different ways four colours could be arranged. Now it acquired a partner. Take Five had one hundred and twenty squares showing all the ways five colours can be arranged. There are five times as many possibilities as there are for four colours. If a sixth colour was added, seven hundred and twenty squares would be needed.  We stopped at five.

Click here to see more about Spacecraft
Click here to see more about Square Snowflake
Click here to see more about Have It All Ways
Click here to see more about Take Five

13c. THE PURSUIT OF AFGHANS continued