The evolution of an Anton Bakker sculpture

This artist’s “canvas” is 3-dimensional space, punctuated by pinpoints of light in a “cubic lattice.” To envision this, think of cubes all exactly the same size, stacked neatly in all directions, matching edges, faces, and corners, to fill space. Then light up the corners, and remove all but these lights—this is the cubic lattice. The artist decides on a path of line segments that connect some of these points, building in certain symmetries, such as repetition, reflection, and reversal.

The instructions for marking out that path (called the “generator”) are encoded in a special language that specifies how to travel from point to point as in “turtle geometry.” (Think of a robot moving in space, directed how to travel to connect certain points.) The coded information is fed into Bakker’s computer program that can search and find thousands of ways in which to repeat and connect copies of the generator to form non-intersecting simple loops, and display images of them. The artist specifies how far these connected paths can venture from the initial point before they must follow a return route to the initial point.

The artist can ask his program to filter the results, choosing (or discarding) those loops that are knotted, for example. He then chooses a few that might have aesthetic potential, and gives life to these “stick figures” or “wire frame forms” by coating them. They can be coated uniformly, making all cross sections exactly the same, all circles, or triangles, or squares. But by smoothing the sharp corners of the stick figures, and varying the thickness and width of the coating, the figures are transformed into sinuous, ever-flowing streams. He can view the results on his screen, turning the virtual figure through every angle to see its symmetries and the 2-dimensional illusions it creates. In the final stage, he decides the size and medium in which to have it rendered as a tangible sculpture.