This simple tutorial shows how to remap an image using the 'UV Coords' attribute of the Image shader to produce an abstract patterned distortion effect. Further examples can be found here.
You can also add a uv_transform shader after the image for extra controls. You could also add a Range shader to further control the distortion effect.
In the UV Coordinates of the Image shader, there are controls for further changing the position of the texture map. When animated, this can produce some interesting results:
Exposure (-10 to 0)