This ‘rule’ predicts that, if the settlements in a country are ranked by population size, the population of a settlement ranked n will be 1/nth of the size of the largest settlement. When settlement size is plotted against rank, on normal graph paper, a concave curve results; plotted on logarithmic scales, a straight line emerges—this is the rank-size pattern.

Many developing countries show primacy: a sharp fall between the largest, primate city and the other cities. The binary pattern, found mostly in federal countries such as Australia, shows a concave curve. The stepped order pattern shows a number of settlements at each level, with each place resembling others in size and function. Fonseca (1989, Institute of Mathematical Geography) explains why the rank-size rule ‘works’. Taylor (2007) GaWC Res. Bull. 238 notes that national urban hierarchies assume that the national urban system is a closed one; relations between cities in different countries are factored out. ‘However, vibrant dynamic cities are always cosmopolitan, [and] to treat New York as US only is to severely under-estimate its economic significance…the national bounding of cities was [always] a critical weakness…it is even more nonsensical today.’