What about
#^2 & /@ {{1, 2}, {3, 4}}
or
N[Sin[#]] & /@ {{1, 2}, {3, 4}}
This following command should add noise to each pixel; well actually to each of the RGB channels.
Manipulate[
Mod[# + RandomReal[delta, 512],
1] & /@ (ExampleData[{"TestImage", "Lena"}] // ImageData) //
Image, {delta, 0, 0.5}]
This gives:
A much more interesting example is given in this fantastic blog post: Doing spy stuff with Mathematica.
M.