This program generates all sorts of polar coordinate drawings based on a seed number. Numbers around 1, (such as .99 or 1.001) work quite well (as do .1, 1.2. You can feed it different seed numbers to get different shapes. Crank up the detail (and the running time) when you have a seed number you like. If the image isn't well centered, or you want zoom in a certain section, you can change the drawing scale. There are also various palette switching options: for stable viewing, for white animation, for pulsating animation, etc.

A program for drawing a cone and a rotating shape are also available.

Click here to download polar.exe.

Visual Basic Version
Several years later, I spent an hour quickly porting the code over to Visual Basic. The drawing part works, but I haven't worked the palette switching in yet. The DOS version is still more impressive.
Here's the source code and executable to a Visual Basic version.

This VB version does not do pallette switching, however: only the DOS versiond oes that, because the Windows APIs to do pallette switching are very complicated.

This is a sample plot

Another sample animation.

This is the main menu of the DOS program