Robert Fathauer
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.
This sculpture is based on the first five generations of a fractal curve. The starting point is a circle, and the first iteration produces a three-lobed form. With each iteration, the number of lobes is tripled. The spacing between features is essentially constant throughout a layer, while the three-fold symmetric boundary of the curve becomes increasingly complex. A hexagonal version of this curve is found in Benoit Mandelbrot's book "The Fractal Geometry of Nature". This hyperbolic surface is reminiscent of naturally-occurring corals. It was inspired in part by a 3D-printed model created by Henry Segerman.
A curvilinear closed form of the dragon curve is depicted (a "twindragon"). The first generation is a circle, and each iteration possesses two-fold rotational symmetry. Curves are shown through 19 iterations.