Power law in language, cities, and wealth — log-rank vs log-frequency is a straight line
Zipf's Law (1949): the n-th most frequent word in a large corpus has frequency ∝ 1/n. More generally, many rank-ordered distributions follow a power law: frequency = C · rank−α. On a log-log plot this is a straight line with slope −α. The law holds for word frequencies, city populations, earthquake magnitudes, income distributions, and more. The mechanism is debated: preferential attachment (Barabási-Albert), Simon's process, optimization under constraints (Mandelbrot), or simply a consequence of the Central Limit Theorem applied to multiplicative processes. Enter your own text to see Zipf's law emerge.
Zipfpower lawlanguagecomplex systems