City size: Spatial dynamics as temporal flows

摘要

For simple systems characterised by two or more dimensions, visual understanding is essential if the number of objects is more than handful. George Miller (1956) argued that this handful was the magical number 7±2 and Herbert Simon (1974) proposed that it was smaller still, being close to what he called a 'chunk', the number 5. This visualisation is concerned with modest numbers of objects, much bigger than a chunk but far, far less than the gigabyte-terabyte magnitudes of big data now being generated. Here, we visualise changes in city size measured by population whose frequency distributions when graphed in counter-cumulative form generate rank-size distributions that approximate a 'power law'. When arranged by size and rank on a two-dimensional graph whose axes are logarithmic, the distribution usually forms a set of points that are close to a straight line. What is hard to represent are changes in size and rank on the same graph, and usually size is dropped. One of us (Batty, 2006) has suggested that we portray rank over time on a clock where time is wrapped around a circle, thus enabling us to say something interesting about different systems and their dynamics (Batty, 2015).