"Digital Diffraction," by Brian Hayes. American Scientist, May-June 1996, pages 210-214.
Many a physics course introduces students to the phenomenon of diffraction by using a lab setup in which one shines a beam of light on a card pricked with tiny holes. This article describes the author's adventures with a computer version of this lab experiment. Although primarily concerned with the physics of diffraction and its computer simulation, the author works into the piece some of the mathematics that arises in this context. For example, in describing the results of his computer explorations, he manages to reveal the heart of the idea of Fourier transforms. In addition, he presents a brief but engaging description of quasicrystals and aperiodic tilings.