The default background for the X Window System is dull, boring gray. If you create a file or a symbolic link (to a file) called $HOME/.Xbackground, the picture in that file will be tiled on your background when you log in. You may use your own favorite scene, pet, etc. or you may use a system-provided image file such as the ones displayed below.
A good background image should be useable on all the screen sizes that you normally work on, ranging from 1024x768 to 1600x1200 pixels. A small tiled image usually works best. None of the ones below are bigger than 512x384, and most are considerably smaller. It helps to have a consistent coloring so that you can find icons hiding against the background. The background should not distract you from your work. And if you work in a public lab or if you have visitors to your office, lurid backgrounds should be avoided because they bother other people.
There are several collections of images on the Linux machines.
To make a symbolic link, use a command similar to this one. Here, the Hankel function graph appearing below is set as the background. Substitute the filename according to your desire.
ln -s /usr/math/X11/backgrounds/hankel.jpeg $HOME/.Xbackground
Here is a collection of backgrounds nominated by the Mathematics Computing Group. Click on each image to see it tiled on your browser's background.