The NAG Blog, to which I contribute from time to time, has a permanent link to Mike Croucher's blog, Walking Randomly. I happened to notice his current article on parametric plotting. The parametric plots are demonstrated with an applet providing Mathematica generated plots and slider controls. Mathematica is a nice piece of software but I couldn't help but think that a modern web browser ought to be able to do this without help from an external application.
I've not used canvas before, but it turns out to be pretty trivial to use, and my attempt is shown below. If you have a canvas enabled browser the plot should appear looking like the plot shown in Mike Croucher's article. Below that should appear some input forms that allow you to change the parameters. These appear as slider controls if a browser understands the HTML5 markup for this (Chrome does in its dev channel version at least). In other browsers they appear as text boxes, which allow you to change the values. (Firefox (4+) and IE (9+) work this way.) The plot should be redrawn if you move the mouse off the form controls.
Actually I prefer the text entry control to the slider, as it is easier to exactly control the value. I'd hoped that the arrow keys could be used to step the slider, but as implemented in chrome at least, that isn't the case. No doubt with a bit more scripting such keyboard shortcuts could be added, but this will do as a first attempt.
e: 0 80
f: 0 80
g: 0 80
h: 0 80
i: 0 80