Category: 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.
reversed metatronic solid (hexahedron)
how to create a piece of art that you can see from all angles?
metatronic solid (tetrahedron)
Three lines make a reversed knot pattern covering all faces of a tetrahedron, regardless of rotation (this same pattern can tile a plane).
self-intersecting tercet knots with encompassment
Three triangular twists are abound together by an encompassing shape echoing the group’s perimeter. The way the paper is cut and overlapped gives the illusion that each of the four main components are made of single pieces of paper. You have to cheat a little to give the illusion of self-intersecting lines made out of a…
encompassed unicursal tercet knot
A hexagonal ring bound to another triply-twisted ring is suspended vertically.
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 (implied) 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…
tercet knot progression with self-similar encompassment
knots entangled with smaller versions of themselves
