Celtic Knots

Celtic Knots have been a fascination of mine for the longest time. Over the years, I have played around with creating simple knots and have developed my own, reliable pattern for producing them. As the more clever of you will soon see, the template for creating knots follows a couple pretty simple rules. The knots I produce rely on a basic weave in the center and wrap around clockwise at the edges.

There is a lot of fantastic math that can be derived from 'knot' problems and they are a curious phenomenon of spatial geometry. Take a look at the pattern below. This is one of my more complex creations that shows just how boggling these knots can be.

How many loops are in this knot? How are they connected?

Here I have highlighted the loops in colour to make it a little easier to see what is happening. Of course, it's still not ideal. But you can begin so see why these knots are so interesting. In fact, you can create knots that consist of a single (highly complex) loop, but those introduce an entirely knew concept. So, to get your feet wet, I've given you a knot that has a lot more symmetry and the pattern is more easily distinguishable.

For those of you who'd like a real clear visual, I have deconstructed this knot into it's basic loops. Essentially 'spilling the beans' on the question posed above, there are 14 loops. They all fit perfectly and snugly together to form a 'somewhat' symmetrical square. How can this be? Certainly, I didn't just stumble across this pattern. This took a lot of thinking and working with these loops and patterns to make it work. But the point is that it totally does work and it opens up a world of possibility for mathematical and creative exploration. Can you make an even better knot than this?