# Douglas Burkholder

Professor of Mathematics
Lenoir-Rhyne University
Hickory, North Carolina, USA

Long, long ago in a place far, far away, my love of art was placed on the back burner as science and mathematics consumed my life. My love for geometry and my desire for visualization for the sake of mathematical understanding have always been central to my teaching and to my comprehension of mathematical concepts. However, only decades later have I begun to explore the artist within and attempted to merge art with my mathematics. Recently I have been investigating how to find beauty in non-periodic tilings.

Penrose Skates
50 x 50 cm
Digital Print
20116

This artwork evolved from a search for beauty and patterns within Penrose’s non-periodic tiling of the plane with kites and darts. Half darts and half kites can be repeatedly subdivided into five smaller components. Start by labeling these five subcomponents A-E. Then, similar to creating the Sierpinski triangle, alternately subdivide and remove all the components with a certain label. After removing tile type A for three iterations we change to removing tile type B for five more iterations. Instead of painting the tiles remaining, pursuant curves are constructed on the regions removed.

Penrose Christmas Lace
50 x 50 cm
Digital Print
2016

Penrose Christmas Lace evolved from a search for beauty and patterns within Penrose’s non-periodic tiling of the plane with kites and darts. Half darts and half kites can be repeatedly subdivided into five smaller components. Start by labeling these five subcomponents A-E. Then, similar to creating the Sierpinski triangle, alternately subdivide and remove all the components with a certain label based upon its location within the five clockwise spirals. After constructing the macro pattern, switch direction of the spirals and iterate several more times to produce the micro detail. Finish by painting all of the half kites red and the half darts green.