knot theories iii

My work is about hidden worlds. This show provides a glimpse into these worlds by answering such questions as: What would overlapping 2-dimensional objects on the same plane look like? Can a single component form wildly different structures? How can a viewer’s perspective reveal a greater range of meaning? Geometric and abstractive works in metal sculpture, painting, woodworking, papercraft and other media illustrate basic principles of topology and tiling.

There is in all things a pattern that is part of our universe. It has symmetry, elegance, and grace – those qualities you find always in that which the true artist captures. You can find it in the turning of the seasons, in the way sand trails along a ridge, in the branch clusters of the creosote bush or the pattern of its leaves. We try to copy these patterns in our lives and our society, seeking the rhythms, the dances, the forms that comfort. Yet, it is possible to see peril in the finding of ultimate perfection. It is clear that the ultimate pattern contains its own fixity. In such perfection, all things move toward death.

From “Collected Sayings of Muad’Dib” by the Princess Irulan

Beauty is for me absolutely fundamental. And it is important. It’s not just an accent. Without beauty we would not do any good science.

Sir Michael Atiyah

  • Pool of the Black Star video

    Pool of the Black Star video

    short film to accompany music by KillDry

  • axonometric tiles

    axonometric tiles

    Lattices of three different colors intersect over a field of triangles. The large hexagon contains the basic unit for the pattern, made up of transformed copies.

  • double quad knot

    double quad knot

    Two knots based on 90° radial symmetry intertwine. The same material (steel) is heat treated with different processes to create two different colors.

  • cistercian counting bands

    cistercian counting bands

    Listing bands with odd and even numbers of twists

  • negative single twist components

    negative single twist components

    A helix and a hexahedron are both composed from a single component, a negative single twist knot.

  • double tri unicursal knot

    double tri unicursal knot

    Rotated copies of two identical outlined knots weave together.

  • infinity knots

    infinity knots

    Five knots are bent into the shape of a larger knot, the symbol for infinity.

  • perspective hex

    perspective hex

    Eight knotted hexagons cover the surface of a cube in a pattern which is identical on each face of the solid.

  • branching unknot

    branching unknot

    Two unknots are arranged vertically above a charred wood base. The shape of the metal makes self-supporting convex and concave arrangements possible.

  • multi-dimensional hex knots

    multi-dimensional hex knots

    Two sets of interlocked hexagonal rings traverse three color fields.

  • woven tile hexahedron

    woven tile hexahedron

    Copies of a single metal tile are woven together to form a cube with a concave vertex.

  • isometric hexagonal lattice

    isometric hexagonal lattice

    A three-hexagon structure repeats to form a lattice made of knots.

  • metatronic solid face (hexahedron)

    metatronic solid face (hexahedron)

    A single shape shows four negative paths curving around the center where they would otherwise intersect.

  • isometric hex knot

    isometric hex knot

    Outlined knot segments are inlaid with copper wire. Each segment follows a path which eventually returns to its origin.

  • unicursal polygonal tercet

    unicursal polygonal tercet

    Stippled paint creates a unicursal knot design. The aggregation of dots suggests straight lines not present in the artwork. This single component is connected end to end with two rotated copies to create the knot. Doubling the individual segments of the knot design does not disrupt the over / under pattern that knot diagrams have.

  • Pool of the Black Star album art

    Pool of the Black Star album art

    album art and some extras for guitar duo KillDry

  • unicursal spiral tercet

    unicursal spiral tercet

    Intersecting spirals become one line. The line can be traced from any point back to its origin.