# Mathematical ImageryMathematical artists create strong, stunning works in all media and explore the visualization of mathematics

# Art Inspired by Mathematics and Nature :: Robert Fathauer

Mathematical structure is evident throughout the natural world. My work incorporates the mathematics of symmetry, fractals, hyperbolic geometry and more, blending it with organic and inorganic forms found in nature. This synthesis allows me to create novel prints and ceramic sculptures that derive their appeal from juxtapositions such as complexity/order and movement/balance.

— *Robert Fathauer*

Ceramics, 25 x 25 x 25 cm, 2018. This piece was inspired by electron micrographs of pollen grains such as dandelion, chicory, and stitchwort. It has approximate icosahedral symmetry.

Sculpture, approximately 6", 2018. This piece is inspired by micrographs of pollen grains, butterfly eggs, and seeds. The geometry, with 60 hexagonal and 12 pentagonal cells, is based on the (1,2) Goldberg polyhedron.

Ceramic sculpture, 17" high. This ceramic 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.

Unglazed porcelain, 6" x 6" x 6", 2015. This is one of a set of unglazed porcelain cubes in five sizes, with a scaling factor of 2 between successive sizes. The set can be used to build a wide variety of fractal assemblies through five generations. This image exhibits the classical fractal known as the Sierpinski Triangle.

Sculpture, 21" wide x 11" high, 2014. This work 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. This fractal structure possesses two-fold rotational symmetry. The sculpture, which was partly inspired by brain coral.

Digital, 2009. "Fractal Tree No. 7" is a digital artwork constructed by graphically iterating a photographic building block created from photographs of the skeleton of a cholla cactus.

Digital print, 15" x 7.5", 2003. This design employs a figure/ground reversal of the same motif in black and white versions from one side of the print to the other. I.e., the eye perceives black dragons on a white background at left, and white dragons on a black background at right. M.C. Escher used this technique in some of his most famous prints, such as "Day and Night". In the center a tessellation of dragons is seen in which no background is visible. In between these extremes the mind's interpretation of what the eye is seeing is not as clear cut. The entire design possesses glide reflection symmetry about a center line if the reversal in colors is ignored.