The Brain as a Recursive Filter

The human brain, being as complicated as it is, does not readily lend itself to be modeled by anything less than gross over-simplification. Nevertheless, one model that I've found particularly useful is to think of the brain as a recursive filter. It receives input from the the outside world in the form of signals that arrive through its various input nerves [1]. These signals then get processed as they pass through the brain, gradually working their way up through higher levels of semantic abstraction until they break through into conscious awareness.
[1]The principal one being the brain stem, but some senses arrive via their own conduit, esp. the eyes, ears, and nose.
A pixelated image of bright colors
The same image, but with black outlines of some objects
The same image, segmented into some oranges, bananas, grapes, and a bowl
The same image; a bowl of delicious fruit
The key construction to note, however, is that this filter is recursive: some (most) of its inputs derive from within itself. If the brain were discretized as a state machine moving from one state to the next, the greater contribution to its next state comes from its previous ones, rather than from whatever stimuli arrive between the two states.
Static perceptual phenomena [2] can be modeled in this context as standing waves; they are in constant motion, however each one passes close enough to its previous state to give the illusion of not moving at all.
[2]Including thoughts, objects, feelings, as well as less pleasant sensations like migraines, obsessions, and seizures.