Lissajoux Motion

The following is the full talk from the MS and US assemblies given by Tim Dolbin, Math Teacher, and his son, Parker Dolbin ’12 about an art project that was developed from the synthesis of math and art, showing the power of understanding and combining many disciplines in a project. 

PARKER DOLBIN ’12:

Hello, everyone. My name is Parker, I am a Waterford graduate of 2012 and recently graduated from BYU with a bachelors in Art. I was asked to come talk about a piece of artwork titled Lissajous Motion that I recently did in collaboration with my Dad, also known as, Mr. Dolbin.

Ever since I was a young teenager, I loved to draw. Whether it was in my notes at school, sketchbooks I would carry around with me, or the countless hours I spent in Mr. Brewers classroom, I was always drawing. As I enrolled in Snow College and then later BYU, my drawing skills not only improved, but my understanding of what drawing is also expanded. I became influenced by artist Brice Marden who had a series of drawings he did with a long stick, standing several feet away from the canvas.  I was fascinated with the work of Tony Orrico and Heather Hansen who held charcoal and used their entire body to create rhythmic movement that resulted in beautiful drawings. I soon became obsessed with pushing my own interpretation of drawing and began to use nontraditional tools to make marks.

It is important for me to note that I was much less concerned with the outcome of these drawings, and more concerned with the process to get there. Sometimes, the outcome of the “nontraditional” drawings were quite terrible, not appealing to the eye, and quite unimpressive. But sometimes, the outcome was the total opposite and even more captivating than the process to get there.

At the same time I was pursuing these ideas, my dad and I went out to Little Sahara Sand Dunes, a dirt-biker’s heaven on earth. With us came a neighbor friend with a paramotor. He filmed us dirt biking while he flew overhead. Afterwords, he showed us the video clips, and I was amazed by the bird’s eye view perspective. I watched as my dirt bike carved these high contrasted lines in the sand and I immediately thought, I need to produce a large scale drawing, using my dirt bike as a tool and the earth as my canvas.

Soon after, I discovered a film and digital media grant at BYU, applied, and received some money to execute the project. Why was I applying for a film grant in order to create a drawing? Again, I was much more intrigued by the process to make the drawing, than I was the actual outcome and filming was a way of documenting that process. I knew I wanted it filmed with a drone, providing a bird’s eye view. I knew I wanted my dirtbike to be my drawing tool. I knew I wanted to do it at the salt flats in the west desert of Utah, another place I often went to ride my dirt bike. I knew that if we timed it right and went only a couple days after it rained, my bike would draw a high contrasted line that would show from a drone filming over 200 ft. above the ground. But I wrestled with what to draw.

I wanted to set more parameters around what I would draw with my bike, rather than just ride around without any real aim. When I told my dad about this idea, he showed me a mathematical curve that ends at its starting point and contained a level of complexity that pushed my idea, but still seemed doable. That curve is called a Lissajous Curve.

MR. DOLBIN:

Lissajoux Curves are formed using “parametric equations,” usually studied at Waterford first in Precalculus 2 and then again in AP Calculus BC. By applying a trigonometric sine wave to parametric equations, the variable of time can be introduced to the traditional Cartesian Coordinate Plane producing a curve in motion. The curve in the two-variable sense is not a function but with the third variable of time acting independently with the variables representing the East/West directions (in other words “x”) and the North/South directions (in other words “y”) it is, indeed, function based.

So we goofed around with different parametric equations, all of which formed Lissajoux Curves, until we selected the one that best fit what Parker had in mind and could be reasonably transferred to the Salt Flat canvas.

The slide your looking at shows the two trigonometric parametric equations (top right) and 75 points on the Lissajoux curve both listed and graphed. We scaled the initial curve coordinates up to fill a 40,000 square foot Salt Flat canvas space and transferred the coordinate pairs into the unit of feet with the positive and negative signs corresponding to North, South, East and West.

In the planning stage we came up with two means of finding the correct location of the 75 points. Remember the space is 40,000 square foot and to draw the curve on the ground with a dirt bike you need to know exactly which direction to ride. We also realized we might spend the entire day setting this up and one “wrong turn” on the bike would ruin the curve. Afterall, there was no convenient “eraser” if we screwed up. Our go-to method was GPS coordinates and our back-up was an old-school compass and 100 foot tape measure. You will see in the video what ultimately worked the best. We placed color-coded flags to mark the travel path. Parker’s older brother Taylor (class of 2010) was the drone pilot and video editor.

And I am happy to report, we nailed it the first time.

ENJOY

Video editor and drone pilot, Taylor Dolbin ’10