Triangular Forms

Noteworthy

Looking through my notes, I have found several instances of triangular shapes that form an interesting group of figures. I have completed a rendering of the triangular form of the Borromean rings, featured earlier in Interlock. This time it's much cleaner and crisp. Here we can see the interlock a bit better and I have also added some woodcut-style shading and some sumptuous color that makes it resemble a real hand-crafted object.

This comes from an original rendering that was done of the triangular rings themselves, but without color and shading. The idea was to make a visual illusion. Without the color and shading it's almost too much to take in all at once. Some confusion sets in.


The Borromean rings are, of course, related to the Valknut. A fantastic impossible Valknut is featured in my blog post Drawing On Your Creativity. My old notes are full of the Valknut and also of impossible figures.

Yet, I have a few pages of handwritten notes where I dwell specifically on triangular figures.

The Borromean rings are remarkable as a three-way-dependent group. If you remove one, the other two fall apart. This is the essence of interlock, of course. The very definition.

Valknut

But the Borromean rings that were used by the Vikings had a very different overlap than this one. And they were usually shown pointing up, not down (though not always).

Here is the correct rendering (though some versions differ in left-to-right reflection from others), with bright colors for each ring. This is clearly distinguished from the first rendering because the insides of the triangles are V shapes.

There are many more ways to show it as well, each with its own overlap formula. If each successive overlap has an over-under-over pattern, though, there are only two, which you see here.

There are two forms for the Valknut, and here is another one. Sometimes this form is called the Triquetra. These two figures have existed for at least a thousand years or longer, in exactly these forms. Most depictions of it on runestones from the Viking age show it as thick and tightly formed. All apparitions of the Valknut are associated with Odin. It is said that it symbolizes Odin's promise that the dead Viking warriors have a place in Valhalla. Those who receive the Valknut are the chosen warriors. So, on thousand-year-old runestones in Denmark and Sweden, you often see a battle scene depicted and a Valknut appears marking the heroic figure.

As far as I'm concerned, though, the Valknut is a cool figure, exhibiting strong interweaving and geometry. My take on this Valknut is that it resembles, at least topologically, the trefoil knot.

Taking it Further

I drew this figure while trying to create a Valknut. But I hadn't allocated enough space for the inner portion, and so I had to join the triangles in the middle. I got another idea or two and sculpted it into its current format.

Isn't it interesting how triangular forms can so quickly become logo-worthy? They catch the eye. This form seems to express that the motion of the form is an internal force, rather than an outwards-moving force. It is closed in on itself, in a way.

One of the main issues with triangular figures is that it forces me to think before I draw. I have to plan ahead.

Here is another figure I drew recently. I think I was onto something with the three points on the right and bottom edge.

With such a triangular network, many possibilities exist. Sometimes I like the irregular forms, because they add character to the shape.

But usually the forms, as they were used in antiquity, were as regular as possible because that form clearly resonated with the ones who made them.

The form I was going for appears to be the Triquetra form with an interlocking triangle.

Inspired

Here is my rendering of this figure, with shadows to make the overlap a bit easier to grasp. By coloring each single thread, the interlocking nature of the figure becomes perfectly clear.

This form becomes almost inspiring in its simultaneous simplicity and complexity. It is no great surprise that this Triquetra form, in various mutations, has been used for so many thousands of years. Though usually the interconnected figure was a circle and the corners were rounded off to make it more like a trefoil knot.

The Book of Kells has one. A runestone on Gotland has a few. With the rise of Christianity in Scandinavia this figure became a cross by connecting four of them (the Carolingan cross). A round Triquetra is used to symbolize the holy trinity on some bibles.

But you can take this format even further. Imagine those who are fascinated by the Valknut (which, to me, symbolizes an idea), separated but entangled by their interest. Here is their symbol.

Nothing can break it.

It's almost like a heraldic mark or insignia.

A badge of fascination.

It shows that the interest for such things never dies. It gets carried on by those who discover the symbol anew. And so it has gone for thousands of years.

Those who practice the art of creating symbology know that there is an inherent interest built right into humanity for what graphic symbols convey to their observer.

The essence and practice of logo forms is rooted in our natural Jungian response to symbols. We can't help our response to them. Yet some logo forms come to stand for evil and other logo forms come to represent eternity. How does this happen? Will these forms forever be etched into our collective memories? The Valknut proves that a symbol can easily last thousands of years.

My sense is that forms are chosen by political groups and companies for a reason. A simple intelligent form can be chosen as a symbol that is easy to remember, to help propagate the brand by creating a catchy figure that can be expressed anywhere. That it can create such a strong impression often testifies to the strength of the designer and their understanding of how we respond to symbols.

Isn't graphic design wonderful?