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Tuesday, October 22, 2013

Knots, Part 3

Knots are also intertwining, and sometimes present a bit of complexity when rendering them. Separate ends may be intertwined, as when we tie our shoes. But loops can also intertwine, and this creates a kind of impossible figure because they are most difficult to actually make. As with Borromean rings and the Valknut, we can also use twists and loops.

In the previous post on knots, I included what I considered to be the simplest intertwining of a loop containing a twist.

Here a gray four-leaf clover loop with twists at the corners intertwines with a brown loop with inside twists. This creates a form of duality because the brown loop is really a four-leaf clover loop turned inside-out. The over-under rule is used on each thread to produce a maximally tied figure. A bit of woodcut shading is also used.

Now I'd like to show a natural extension of the figure eight intertwined with a simple loop. I designed this form a few days ago, but it took me a few days to get to a proper rendering. I used the same techniques to produce this as I used in the examples from the previous post. Except that I used a spatter airbrush on a gel layer to create the shading when one thread passes under another.

I used a simple airbrush on a screen layer to create the ribbon highlights. As always, I wish I had more time to illustrate!

But this figure shows how four loops can become intertwined in an interesting way by twisting each loop once.

Each knot I draw starts out as a thin black line on a page. I don't even worry about the crossings and their precedence. I just try to get the form right. The final result is very complex and simple at the same time.

Knots have their stylistic origins in antiquity. They were used for ornament and symbology by the Celts, the Vikings, and the ancient Chinese.

A purple loop with three twists intertwines with a blue circle in this knot.

The shines were created using a lighter, more saturated color and mixed into the gel layer using the Just Add Water brush in Painter. It's a bit like a Styptic pencil and was one of the first mixing brushes I created in Painter in 1991.


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