Laser Light Math: Music to the Eye
Merrill J. Lessley (UCB)

These images of mathematical "curves" were constructed by reflecting argon and helium-neon laser beams--red, blue, and green frequencies--off of rapidly moving computer controlled first-surface mirrors.
This “sequence” of laser images is the product of research regarding the design and construction of a computer-controlled laser projection system. The system can be used to precisely shape or graph a variety of mathematical curves (epicycloids, hypocycloids, roses, epitrochoids, hypotrochoids, and other special sine/cosine cases). By graphing such curves, a wide variety of appealing images can be created. Unlike drawing them with a pencil on paper, however, projecting such curves with a laser poses a particularly challenging problem. While a laser is often referred to as a kind of “pencil” in light, it can only be used to generate a complete picture by moving its projected “dot” rapidly and repeatedly over a reflective surface. Thus, the visual presentation of any complete laser image, like those shown here, requires a projection system that can move a laser “dot” continuously and rapidly through a selected mathematical pattern. Each pass through a pattern constitutes a single “scan.” To work properly, at least fifteen such scans must be completed every second. The images shown here were scanned at about three hundred times per second. With this manner of projection, our “persistence of vision” transforms a small dot of moving light into what appears to be a solid line or pattern. Interestingly, when that pattern represents one of many intriguing mathematical curves, beautiful images in moving light appear that are simply … “Music to the Eye.”