The buttons on the Demos panel are defined in the file basic-demos. It is easy to customize your own Demos panel by simply having a different basic-demos file in a directory ahead of the demos directory in the KnotPlot path.
A brief description of each demo is given below, click on the demo name to see the file that defines it. One caveat is in order: when running the demos it is best to allow a demo to finish before clicking on another demo button. If you don't follow this advice, unpredictable (but harmless) behaviour may result.
The Monster is a famous unknot, called a monster by Louis Kauffman (load Monster and go Monster). This relaxation is also available as an MPEG movie at the knots page in the KnotPlot Site.
Fig4 is another nasty unknot about which I will soon have more to say. (load Fig4 and go Fig4).
The last precomputed relaxation is that of a six-component Brunnian link. The final state of this link can be seen in all its raytraced glory, floating deep beneath the sea (load Brun and go Brun).
VanKampen Zeeman and Andrews Curtis create linked (but individually unknottted) spheres in 4D. You need to go to the 4D Control Panel to do anything with them. The first of these links is featured on its own page at the KnotPlot Site.
The 4D torus demos are all variations on displaying a 4D torus. You can read about this torus on a page by Thomas Banchoff.
Trefoil 1 is a trefoil knot, created with the conway command, relaxing with collision checking turned off, undamped dynamics, and leaving a trace. This can be fairly wild in stereoscopic 3D.
Paint 1 and Paint 2 set things up to use a trefoil as a 3D paint brush. After clicking on these buttons, try clicking and dragging all three mouse buttons in the View Window. Paint 3 will setup painting mode with whatever you currently have loaded. A page explaining the use of KnotPlot as a paint program is under construction. Some paintings can be seen at the KnotPlot Site.
Wings and Negative Cylinder Space are more examples of interesting effects that can be achieved by setting paramters out of range. After clicking on Wings, you might want to go to the Main control panel and try changing 'broff', 'nseg', or 'ncur' with the sliders. Click on the 'twfix' button on that panel to make things nice. The Negative Cylinder Space will give you something slightly different each time you click on it.
The Flower button gives you something different each time (some of them are not so nice). These flowers can be somewhat decorative. As a blast you can also startup KnotPlot with the -flowers command line option.
I'll leave the rest of the extra demos for you to figure out. If you get KnotPlot into a weird state, you can (probably) recover by entering a `reset all' command (or clicking on the Reset button on the main demos panel).