hidden worlds

This exhibition is based on the paper presented at Bridges 2023 and the 2024 Knoxville AMA conference, “Surface-tiling Curves.” The subject is the application of a space-filling curve segment to the faces of regular polyhedra. The work represents real-world examples of time slices in the iterative process of these curves as sculpture and print.

Each piece exists as snapshot along the way from one to two dimensions. Glimpsing into these hidden worlds is a way of looking deeper without looking closer.

  • surface-tiling curve hexahedron set (И 1-4)

    surface-tiling curve hexahedron set (И 1-4)

  • surface-tiling curve octahedron set (И 1-4)

    surface-tiling curve octahedron set (И 1-4)

  • surface-tiling curve (alternating iteration) construction diagram

    surface-tiling curve (alternating iteration) construction diagram

  • surface-tiling curve labyrinth

    surface-tiling curve labyrinth

  • knotted surface-tiling curves for hexahedron И 1-4

    knotted surface-tiling curves for hexahedron И 1-4

  • triangle-based surface-tiling curve iteration segment overlaps

    triangle-based surface-tiling curve iteration segment overlaps

  • surface-tiling curve hex band

    surface-tiling curve hex band

  • triangle tile-based surface-tiling curve listing band (И 3)

    triangle tile-based surface-tiling curve listing band (И 3)

  • triangle-based surface-tiling curve segment intersection

    triangle-based surface-tiling curve segment intersection

  • encompassed surface-tiling curve segment

    encompassed surface-tiling curve segment

  • surface-tiling curve deltahedron set (И 3)

    surface-tiling curve deltahedron set (И 3)

  • cube sliced by surface-tiling curve

    cube sliced by surface-tiling curve

  • exploded tetrahedron divided by surface-tiling curve И 1

    exploded tetrahedron divided by surface-tiling curve И 1

  • exploded hexahedron tiled with a plane-filling curve

    exploded hexahedron tiled with a plane-filling curve