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One way to create knot patterns is to use a set of tiles that are put together following a few basic rules. This is not, as far as I know, a standard way to create these patterns - the book by Aidan Meehan, provides a technique for drawing the patterns by hand, rather than laying them out as tiles.
A wide range of knot patterns, including the one shown above, can be created using the set of six tiles shown below. These were constructed using Geometer's Sketchpad.
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When laying down the tiles, you have the option of rotating them - some of the tiles don't alter with rotation, some of them can be placed in two ways, some in four.
A nice property of this set is that you can't paint yourself into a corner when using it - you can always find a tile that will compose with the pattern that you have started. This property means that this set of tiles is closed, in a certain sense.
A wider range of patterns can be created if you add tiles like the ones below to your set.
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The knot pattern below (better described as a woven set of three links) was made using tiles including the ones from the "extended" set above.
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