You can add randomness to any property as it varies over time by using The Wiggler. You can also use the wiggle expression to accomplish this. (See Property attributes and methods.) Depending on the property and the options you specify, The Wiggler adds a certain number of deviations to a property by adding keyframes and randomizing interpolations coming into or out of existing keyframes. You need at least two keyframes to use The Wiggler.
Using The Wiggler, you can more closely simulate natural movement within specified limits. For example, add randomness to an animated butterfly to produce fluttering. Add it to brightness or opacity to simulate the flicker of an old projector.