x = exp(−At)·[sin(a_{1}t + b_{1}) + sin(a_{3}t + b_{3})],
y = exp(−Bt)·[sin(a_{2}t + b_{2}) + sin(a_{4}t + b_{4})]

Maybe you're already familiar with Lissajous figures (Bowditch curves). These can be realised by any oscilloscope or even with refined mechanical pendulums (harmonographs), cf. woodgears.ca or karlsims.com, whereby of course potential energy is lost: the pendulum comes to a standstill (parameters A and B below).

The figure to start with comes with a big stepsize, if you reduce it you'll get a smoother graph.

Just vary the parameters! Hint: Click on the parameter sliders and control the change via your cursor keys. Have fun!

In case this application does not work in your device, check my GeoGebra version (.html). In any case, JavaScript has to be activated in your browser.

If you like to create a vector graphic, you can use my small python program (.py). Or try this:

Save as SVG (for tiny computing keep stepsize big and t small!):