Long exposures can be used to produce wonderful abstract images created by movement of either the subject or the camera. The image on the right clearly shows fireworks, but crop it so that the frame is filled by the patterns at the upper left and the subject becomes more abstract in nature.
This picture was taken with the camera mounted on a tripod, but other more abstract variations may be created by hand-holding the camera or even moving it during the exposure period. With practice, all sorts of interesting curves and wiggles can be created.
There are no correct or incorrect approaches to this sort of photography. It is up to the photographer to use his or her imagination and be prepared to experiment with a subject. Try photographing a forest of tree trunks and panning the camera in the vertical plane during the exposure. The result should be a pleasantly blurred series of smooth tree trunks with a hint of green vegetation in the background. Whether the original subject is recognized by viewers depends to a large extent upon the degree of blurring.