Definition: In mathematics, a Lissajous curve , also known as Lissajous figure or Bowditch curve, is the graph of a system of parametric equations.
definition and equation credits to the wikipedia page http://en.wikipedia.org/wiki/Lissajous_curve
The figure is sensitive to the ratio of a and b.
I have made a small change. Instead of a continuous line, I have taken points at regular intervals and joined them. For certain numbers of “a” and “b”, some interesting shapes were seen. I have attached some of them below.
It took some time and luck to arrive at these, so I cannot publish the equations here.