This applet will help you experiment with the symmetries of patterns made by parametric equations of the form
(t + An sin(nt) + Bn cos(nt), Cm sin(mt)+Dmcos(mt) )
To create a term for an expression of this type, enter the coefficient and frequency in the labelled boxes and use the checkboxes to select whether you want a sine or a cosine term added to the expression for x or y. Then click the "addterm" button. If you don't like the result, use the "remove last term" button. To see the picture formed by the parametric equations (x,y) and (x,-y) at the same time, press the "mirror" button, which works as a toggle.
For purposes of horizontal scaling you can alter the coefficient of the t term in the expansion. To do this enter the desired coefficient in the box and click on Set tcoeff.
This applet was created as part of the experimentation that led to an article "Woven Rope Friezes," by Frank Farris and Nils Kristian Rossing, appearing in the February, 1999 issue of Mathematics Magazine. The attractive images for that article are available online.