Josh and I created this applet for a Linear Algebra project in computer graphics. It allows you to draw shapes and perform geometric transformations. The matrix representation of the transformation is also displayed. It also features color rotation for each transformation and the ability easily repeat a transformation thousands of times. It's great for making cool patterns :)
AppletJava 2 compatible browser, plugin, jdk/sdk, or jre. If you don't already have one, be ready for a big download. If you have a mac, your out of luck; Java 2 support isn't expected until Mac OS X comes out in mid 2001. Porting the applet to Java 1.1 would be a pain, because it makes heavy use of the new Java 2D API (AffineTransform is our friend).
Here are some links:Download everything at once: Unix Mac Windows
TransformApplet.java - the main applet and UI code
DrawPanel2D.java - component that lets you draw shapes and transform them; the real meat of the app is here
MatrixPanel.java - component to display matrices. very klugy for now, needs to be made more general!