Spirotechnics are based on Spirographs--the old toys that have a gear within a gear, and draw crazy designs. Several years ago, I had an idea: what would happen if you put a spirograph inside another spirograph? As you can see, the results are spactacular and diverse.

​

      For those who are interested in the technical information: Spirotechnics are defined by parametric equations that are a linear combination of sine functions (in the y-direction) and cosine functions (in the x-direction). In order for the circles not to "slip" in relation to each other as they rotate (simulating the gears on a spirograph), the ratios of the rotation of each circle is depends on its motion relative to its outer circle. Aside from this constraint, there is a large amount of flexibility in the system, which allows for the countless different Spirotechinic designs. The color of the graphs is usually determined by the speed point being drawn, though it can also be based on the acceleration or direction. Animations are produced several several ways, but my most common method, is to draw an entire graph, then rotate one of the circles a few degrees and repeat until the circle returs to its original orientation. 

 

The Spirotechincs program was written in Java using the Processing graphics library.