  It is a well observed phenomenon that natural images are smooth, in the sense
that nearby pixels tend to have similar values. We describe a mathematical
model of images that makes no assumptions on the nature of the environment that
images depict. It only assumes that images can be taken at different scales
(zoom levels). We provide quantitative bounds on the smoothness of a typical
image in our model, as a function of the number of available scales. These
bounds can serve as a baseline against which to compare the observed smoothness
of natural images.
