knot theories

This work was on display during March, 2021 at The Emporium Gallery in downtown Knoxville.

Knots are continuous lines twisted in such a way to give the illusion of lines overlapping in the same plane. Using a formalized system of knot creation, the artwork here represents knots in multiple “in-between” dimensions in three categories, each based on a partial dimension:

– unicursal, self-contained lines which appear to overlap on two-dimensional surfaces (unicursal knots)
– knots on tiled surface planes of regular polyhedra (metatronic solids)
– elements of non-orientable surface segments (listing bands)

Each piece is based around a simple line or shape translated or rotated to create more complexity. Light and shadow are an important element, so artworks appear different in their environment depending on the time of day. The shapes and symbols they create are purely geometry, with no hidden meaning beyond the beauty of intricacy.

chatoyant tercet knot

the quintessential knot
triple knot listing band

three braided knots as a listing band
translucent listing band slice stack

Perfectly symmetrical listing bands are difficult to display because of one of those things that bring us all down, like gravity. But, if you could slice one (or really anything that’s hard to balance) up, you could stack the slices and create the illusion of a dimensional solid. The video explains a lot: The first…
collapsible scale listing band (deconstructed)

deconstructed listing band segment
reversed metatronic solid (hexahedron)

how to create a piece of art that you can see from all angles?
metatronic solid faces

isolated polyhedra faces
metatronic solid (tetrahedron)

regular polyhedra tiled with knot patterns
tercet chain knot

copper knot inlaid in wood
self-intersecting tercet knots with encompassment

You have to cheat a little to give the illusion of self-intersecting lines made out of a single piece of paper….
encompassed unicursal tercet knot

Ideal viewing conditions for this piece: strong sunlight with a nearby shadow to reflect in.
projected isometric tercet knot

This is a double-lined, triple-component knot based on an isometric grid. The rules of knot making are slightly bent with the double line, but half the fun of making your own system is breaking its rules. It is “projected” is because its construction uses small wooden dowels to lift the individual pieces above the surface.…
unicursal pentad knot

Follow the line with your eye. The line is unicursal, meaning there’s only one line. At first you might be tempted to assume there are five sections, and of course there are, but the radial symmetry is just a property of this particular line. These are probably the most difficult knots to design because you…
tercet knot progression with self-similar encompassment

knots entangled with smaller versions of themselves
axonometric scale listing band

the question Is there a shape, which when repeated, can create a Mobius strip? Yep, there is. Really all you have to do is chop up a strip into squares, however many pieces you want and there you go, done. That was easy. Maybe I’m not asking the right question. the better question Is there…