Applications and explanations of Zipf's law

Recently I have been intrigued by the reappearance of an old friend, George Kingsley Zipf, in a number of not entirely expected places. The law named for him is ubiquitous, but Zipf did not actually discover the law so much as provide a plausible explanation. Others have proposed modifications to Zipf's Law, and closer examination uncovers systematic deviations from its normative form. We demonstrate how Zipf's analysis can be extended to include some of these phenomena.