Frank A Farris

Professor of Mathematics and Computer Science
Santa Clara University
San Jose, 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 new 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.

Earth and Fire Animate the Body
51 x 61 cm
Digital print on aluminum

I modified a simple formula for creating regular polyhedral meshes from a symmetric set of points and arrived at the "shrink-wrap" appearance of the dodecadedral shape, rendered here in granite and in crystal. (The input to the mesh algorithm is the set of dodecahedral face centers.) The sphere is decorated with the same symmetry, using a collage of flower photographs as the base image. I placed a copy of the sphere inside the crystal shape, aligning by symmetry, and waited about a day for ray tracing to create all the marvelous reflections. The tromp l'oeil frame uses Fourier series, a photograph of wood grain for texture, and more hours of ray tracing. For me, the scene evokes the synergy of elements that give us life.