This design is made up of dragon curves of different sizes fitted together.
A dragon curve is the shape produced by folding a long strip of paper many times and then opening it out so that each fold becomes a right angle.
This afghan contains dragons of different sizes. Each one is made from two strands of yarn - a main colour to distinguish the dragons from one another and a more subtle tone which depends on the dragon's size.
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SPACE-FILLING CURVE AFGHANS
SPACE-FILLING CURVE CUSHION
The background is a filet crochet grid (or you can use square-mesh fabric).
The dragons are applied with surface crochet.
Applying the first dragon needs a lot of concentration. Once the first is in place, the others are much easier as they twist round each other.
We made two versions. One is on a dark background with mohair dragons.
There are four main colours and each different size of dragon has another colour mixed with it to denote its size.
The other version has a white background and chenille dragons in four colours.
Take a l-o-n-g strip of paper and fold it in half, half again and half again. Open it up and crease it firmly on the folds, taking care not to bend them in the wrong direction. Stand the paper on its edge with each fold forming a right angle. This is an Order 3 dragon (because the paper has been folded three times) You should see shape 3 when you look down on it. If you turn over the strip of paper, the dragon will be going in the opposite direction.
Make as many folds as your paper allows, always folding in the same direction. Order 4, 5 and 6 dragons are shown opposite.
You will soon be unable to make more folds in the paper and, if you want to know what would happen next, you will have to work out the folds for further dragon curves. For more details of the mathematics involved in drawing the dragons see Dragonometry.
The large dragon (which is not drawn to the same scale) is what you would get after the 9th fold. The corners of the paper often meet but they cannot cross. On this drawing the corners have been rounded so you can see which parts are joined and which are merely touching.
Dragons can be fitted together in many different ways.
Click here to read a magazine article about mathematical knitting and crochet, including Curve of Pursuit.
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