# Robert Fathauer

Small business owner, puzzle designer, author, and artist

Tessellations Company

Phoenix, Arizona

I’m fascinated by beautiful and complex forms both in mathematics and in the natural world. Combining mathematics with artistic creativity allows me to explore and express these ideas in unique images and forms.

Duals

12" x 6" x 6"

Ceramics

2012

The cube and octahedron are duals of each other. In these two pieces, an octahedral frame encloses a cube and a cubic frame encloses an octahedron. The contrasting colors in the frames and enclosed polyhedra are due to the fact that they are made from two different types of clay. Neither was glazed, so the natural appearance of the fired clays is seen.

Hyperbolic Fractal Tiling No. 1

18" x 24"

Archival Inkjet Print

2012

This digital artwork features four views of the same three-dimensional object, a fractal tiling in which every tile is a similar dart shape. The starting point is a pair of tiles matched along one long edge. A pair of smaller tiles is fit into each of the V-shaped openings in these starting tiles. The sum of the angles at each vertex where two of the smaller tiles meet a larger tile is greater than 360 degrees, so the three tiles cannot lie in the same plane. The pairs of smaller tiles alternately buckle up and down to accommodate the fit. This same simple rule is applied repeatedly through ten generations, resulting in the object shown. This object was created in Mathematica, and PhotoShop was used to create the montage. This is a demonstration of the way in which a complex organic structure can result from a simple set of rules being applied over and over again to a simple starting structure. The resulting object is an intriguing blend of the organic and the geometric.