2015 Joint Mathematics Meetings
Robert Fathauer
Artists
Robert Fathauer
Owner
Tessellations
Apache Junction, Arizona, USA
Statement
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 natural world is shaped by mathematics, so that geometry underpins organic structure. My more recent work blends geometric and organic character in abstract forms.
Artworks
This sculpture is based on the first three generations of a fractal curve that develops radially outward. The starting point is a simple saddle, and the final form has an envelope that is roughly hemispherical. The space curves were created by fitting a series of planar fractal curves to the surface of an octahedron and then distorting them to fit a deltoidal icositetrahedron. Half of that structure, possessing two-fold rotational symmetry, was used as a model. The sculpture was partly inspired by brain coral.
This sculpture is a fractal tree carried through five generations. With each iteration, the number of branches is tripled. The scaling factor from one generation to the next is the inverse of the square root of 3, approximately 0.577. As more and more branches are added, the top surface begins to display the classical fractal known as the Sierpinski triangle.