Diigo pointed me to this interesting web page, Flower Maker.
You can start with a blank canvass, or load someone else's flower to work on. Choose how many petals you want in your flower, then the opacity (transparency) of the petal, then the shape and color. Now drag your mouse across the canvass and see what happens.
If you don't like how it looks, you can undo your last stroke, or start over.
When you click the save button, name your flower, and it is entered in the gallery for other people to see. If you want to save it to your computer, take a screen shot, and then open it in a photo editing program (such as Photofiltre), crop it, name it, and save it.
I think this is a great web page - it's easy to create very complicated designs, and explore symmetry, color, line, shape, and design.
My only regret is that the left and right side of the page contains advertisements. Students should be advised in advance about them, and a teacher might want to check out the page to see what ads appear. One solution is to save the page to your computer ("Save as...web page complete"), and then open the swf object you'll find in the page elements' folder in your web browser.