I have to admit, sometimes the mathematical premise behind my quilt makes some sense and other times I just can't get my head around it. Sadly, today is one of the later. My head is already starting to hurt, as so many of you have already expressed as a common reaction to higher math.
The imagery comes from Fourier Series and phasor vectors. The idea is relatively simple sine waves are added together in different phases to form more complex curves. These can be expressed with mathematical equations, or visually in a complex plane or periodic signal. I used the website Phasor Phactory to create visuals for one of these complex waves. The large image is the wave on the complex plane. The quilting lines are the periodic signal of the same wave. This is definitely a case where an artist rendering is much easier to understand than the mathematical explanation!
I did a lot of firsts for me with this quilt. I used traditional piecing for the background quadrants, but then fused the shapes within the curves. I also fused shears where the outline of the curve made a loop. I then used free motion zigzag to follow the line of the curve. Finally I did precision quilting to follow the exact periodic signal of the wave. I'm not one who usually follows a pattern--I tend to be very loose in my quilting--so sticking to the lines was rather difficult. My first attempt was awful, so I ended up redoing the whole quilt. I tried to use a plastic film as a guild, which I stitched over. In my test, it perforated fine and I was able to pull out the pieces. The problem was the tension was a mess with more bobbin than top thread showing. I solved the problem the second time by using water soluble stabilizer and the same bobbin and top thread. Here is a close up of the stitching so you can follow the lines of the curve.