GeoGebra is a great tool for learning and teaching mathematics. It also caters to frustrated artists like me.
Click on the check boxes to show the parabola, sine, ellipse and the geometric objects in the order given. Enjoy my AngelGebra. Click the refresh button to redraw. If you want to create your own, see Dancing Graphs for patterns.
[iframe http://math4teaching.com/wp-content/uploads/2012/02/curve_art.html 600 550]