Doug Dunham, Lisa M. Shier

Statement

Our goal is to create artworks that have interpretations in hyperbolic geometry, the Poincare disk model of the hyperbolic plane in particular. We have obtained inspiration from the Dutch graphic artist M.C. Escher, among others. One of the machines we used to realize our artworks is a computer-controlled paper cutter/plotter/scorer. The latter machine has a single pen that can be used to draw designs on pieces of paper before cutting. The paper we use comes in a variety of vivid colors, which adds to the aesthetics of our artworks. In addition to paper, there are sheets of foam that can be cut by the cutter and applied to the back of a previously cut piece of paper of the same shape in order to raise it above the background.

Artworks

The Dutch artist M.C. Escher realized his "angels and devils" pattern in each of the three classical geometries: the Euclidean plane, the sphere, and the hyperbolic plane. Those works were Regular Division Drawing #45, "Heaven and Hell' on a carved maple sphere, and his woodcut "Circle Limit IV", respectively. In the latter two works he specified "heaven" and "hell" regions by: 1) indenting the devils and raising the angels in the heaven region (and the opposite for the hell region), and 2) showing all interior detail of the angels and no interior devil details in the heaven region (and the opposite in the hell regions), respectively. We have designed a hyperbolic pattern that combines these methods, thus creating a 2.5D artwork.