James Mallos

Statement

I am interested in simple descriptions of surfaces and shapes. Woven structures are a practical bridge between surface and shape: they are shape shifters that can take many conformations, but they tend to favor one with minimum bending energy. In this work I am interested in making corrugated baskets, that is, baskets where each opening in the weaving plays a role in the miniature landscape of the basket's surface, either as hill, dale, or saddle. For simplicity, it is desirable to make a basket from single, unicursal strand. Such a basket is, mathematically speaking, a knot. Large knots being hard to tie, I have developed a technique where the strand clips to itself at crossings without need to go over-and-under.

Artworks

A knot projection on the sphere is special if every Seifert circle is innermost. Orienting the knot induces an orientation around each region of the projection: clockwise, counterclockwise, or alternating.  Coloring these regions as hill, dale, and saddle, gives a terrain where the knot can be traced by a closed geodesic. To see this geodesic, I made a basket using a straight strip that follows the path of the 7-4 knot’s projection, and then splices to itself. Saddle openings have angular deficit, non-saddle openings have angular excess. Hill openings are forced convex, and dale openings concave, as each is completed. The strip’s centerline marks the geodesic. This is an ascending knot with the same projection as 7-4.