Robert Fathauer

Small business owner, puzzle designer, author, and artist
Tessellations Company
Phoenix, Arizona, USA

I'm endlessly fascinated by certain aspects of our world, including symmetry, chaos, and infinity. Mathematics allows me to explore these topics in distinctive artworks that I feel are an intriguing blend of complexity and beauty.

The laws that govern our physical universe can be succinctly expressed by mathematical equations. As a result, mathematics can be seen throughout the natural world, and much of my work plays on mathematical forms in nature.

Five Iterations of a Trefoil Knot, Four Views
Five Iterations of a Trefoil Knot, Four Views
50 x 50 cm
Digital Print

This three-dimensional iterated knot was created from a two-dimensional design called "Infinity", from 2006. A starting projection of a trefoil was used that has two loops within a loop. This provides a self similarity that allows iteration by placing two smaller copies in each of the small starting loops. With each generation, the number of loops added doubles. The iteration process can be continued indefinitely, with the structure remaining a single strand.

Icosa Form
Icosa Form
30 x 30 x 30 cm

This abstract sculpture, which mixes biological and geometric forms, is based on a regular icosahedron (solid with 20 faces). Natural forms that influenced this piece include starfish and diatoms.