How to Draw a Complex Knot
 

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This knot looks quite challenging and to draw it from a scratch is not a simple task. But don't get put off by its apparent complexity. There is a way to construct this relatively easily.

 

Here is how you can construct one.

To start off, pick a square.

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Draw any modular knot you fancy, making sure that the arbitrary distances specified are kept strictly equal on all 4 sides. This is crucial in alignment of knots in the later stage.

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Once this is done, you can immediately create a knot based on grid system. That is, by arraying the knot module 4 times around the red circle

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Continue on with the arraying procedure until you get the desired numbers of modules and by eliminating the squares around the modules you will achieve the following.

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However, if mirroring is adopted rather than the arraying procedure, you will obtain something still different

After several operations, the result will be something like this:

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Thereare other possible configurations; Going back to the first knots, we need a equilateral triangle based knot module shown below together with the square based one.

Pay particular attention tothe alignment between the 2 different modules.

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Now, it is possible to tile a plane using only squares and equilateral triangles. There are a few examples of this. But for the sake of showing what this method is capable of, only one example is used here.

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The next step is to replace all these squares and triangles with the square and triangle knot modules that we have worked on. The result is the following:

Now you have to erase all the triangular and square frames to expose just the knots chain.

This method can be utilized to produce many complex knots. It is interesting to observe the relationship between tessellations and knots. This opens up new area of tessellations that study the number of possible tiling combination using squares and equilateral triangles.

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