Frank A. Farris

Professor of Mathematics and Computer Science
Santa Clara University
Santa Clara, California, USA

Twenty years ago, all I wanted from my art was to make better wallpaper patterns for my geometry class. Now I take delight in being carried away in the worldwide mathematical art explosion. I hope my work illustrates the joy and beauty that mathematicians have always experienced, but only recently have had means to make visible.

Now in a post-wallpaper period, I’ve found more general techniques to put patterns on surfaces, using meshes, texture maps, and ray-tracing. The consistent toolbox is mathematical analysis: solutions to PDEs and complex functions give a surprisingly flexible artistic vocabulary for creating surprising shapes as well as marvelous patterns to decorate them.

Clam Landscape: A Mathematical Surrealism (CLAMS)
41 x 51 cm
Digital print

The shells for these giant clams started as Fourier series for a shell outline in the plane. The shapes were popped up into 3D with tricks of cylindrical coordinates. The outer shells are decorated with a photograph of startlingly blue water in China Cove near Carmel, CA. The inner shells rosettes use a spherical photograph of stained glass in St. John’s Abbey in MN. The pearl pattern draws on the interior of the Basilica of St. John in San Jose, CA and spherical harmonics with icosahedral symmetry. The virtual frame comes from more Fourier series, one series for the outline, another for the cross-section, which gives the ribbon texture. The (real) background is a reef display in the CA Academy of Sciences.

3D Printed Clam Shells on Stand
10 x 18 x 18 cm
Coated Full Color Sandstone

The top and bottom halves of the clam shells pictured in CLAMS have been printed in Coated Full Color Sandstone. Sitting on a rotating mirror stand in front of the printed scene, they increase the sense of surrealism. We are seeing the very things whose existence we doubted in the magical digital image. Although the shells in the posed scene appear to be infinitely thin at the edges, each one actually thickens gradually toward the middle. This was done using different top and bottom surfaces that meet in a sharp edge, so there are four surfaces in all. Holding the two shells apart is a 3D printed sphere decorated with a Fibonacci spiral.