This paper presents an approach to urban dynamics that generalizes the traditionalrank-size model first popularized by Zipf (1949). It argues that we need to define the rate atwhich new cities emerge and old cities disappear within the apparent macro stability posed byZipf?s Law. We illustrate this with a reworking and extension of Zipf?s analysis of the USurban system, taking his analysis from 1790 to 1930 forward to the year 2000. In doing so, weintroduce a variety of devices to detect urban change based on traces through the rank-sizephase space, trajectories using a rank-time clock, and the definition of urban half-lives. We setthis analysis within the wider context of stochastic simulation that is currently dominatingdiscussion of scaling processes such as these
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