One cool way to generate Zipf's law is through random growth. See an example here for the distribution of cities: https://academic.oup.com/qje/article/114/3/73

One cool way to generate Zipf's law is through random growth. See an example here for the distribution of cities: https://academic.oup.com/qje/article/114/3/739/1848099 https://academic.oup.com/qje/article/114/3/739/1848099 The idea is that if the growth rate of a city is drawn from the same distribution, regardless of the actual city size, we get Zipf's law. To me this is a reasonable explanation why we see Zipf's law in many places in nature.