Merrill Lessley and Paul Beale

"Laser Light Math1: Music to the Eye"

Laser images were first captured in high-resolution video and then moved to single frame digital photos. MOV clips available (dynamic and beautiful),
8.5" X 11", 2006-2007.

"Laser Light Math1" was constructed by scanning three lasers with sine/cosine signals. The base image requires a mathematical approach similar to those used to graph traditional curves (like hypotrochoid or epitrochoid). However, unlike graphed representations, this image requires rapidly moving laser dots. Thus, common equations are modified to accommodate the "dynamic" nature of the process. While the traditional formula for a hypotrochoid curve starts with x=(a-b)cosT, here we use x=(a-b)*cos(omegaO*T). OmegaO=2*pi*(base frequency). Frequency is how often (per second) the laser completes a single sine/cosine scan. "T" is whatever wave synthesis step (1 to 512) the sine or cosine function is at.

"Laser Light Math2: Music to the Eye"

Laser images were first captured in high-resolution video and then moved to single frame digital photos. MOV clips available (dynamic and beautiful),
8.5" X 11", 2006-2007.




"Lessley2" was constructed by scanning three lasers with sine/cosine signals. Constructing the base image requires a mathematical approach similar to graphing (Cartesian) the hypotrochoid curve. However, unlike simple graphed representations, this image requires the use of rapidly moving laser dots. Thus, the common equation is modified to accommodate the "dynamic" nature of the scanning process. While the traditional formula for a hypotrochoid curve starts with x=(a-b)cosT, here we use x=(a-b)*cos(omegaO*T). OmegaO=2*pi*(base frequency). Frequency is how often (per second) the laser completes a sine/cosine scan. "T" is whatever wave synthesis step (1 to 512) the sine or cosine function is at.

"Laser Light Math3: Music to the Eye"

Laser images were first captured in high-resolution video and then moved to single frame digital photos. MOV clips available (dynamic and beautiful),
14" X 14", 2006-2007.



"Laser Light Math3" was constructed by scanning three lasers with sine/cosine signals. The base image requires a mathematical approach similar to graphing a special case (rose) of the hypotrochoid curve. The Cartesian equation is modified to accommodate the "dynamic" nature of the scanning. While the traditional formula for a hypotrochoid curve starts with x=(a-b)cosT, here we use x=(a-b)*cos(omegaO*T). OmegaO=2*pi*(base frequency). Frequency is how often (per second) the laser completes a sine/cosine scan. "T" is whatever wave synthesis step (1 to 512) the sine or cosine function is at. Additionally, a=(2n)*h/(n+1) and b= (n-1)/(n+1*h. ("h" controls image size). "n" is the number of petals.

Merrill Lessley and Paul Beale
Merrill Lessley is a professor in the Department of Theatre and Paul Beale is a Professor in the Department of Physics
at the University of Colorado at Boulder

Merrill Lesslet lives in Longmont, Colorado, USA and Paul Beale lives in Boulder, Colorado, USA

"These "sequences" of laser images are the product of interdisciplinary research regarding the design and construction of a computer-controlled laser projection system. The system precisely shapes or graphs 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. The images shown here were scanned at about three hundred times per second. Interestingly, when that pattern represents one of many intriguing mathematical curves, beautiful images in moving light appear that are simply ... 'Music to the Eye.'."