Zipf's Law and Information Complexity in an Evolutionary System

Zipfs law is a famous empirical law that is observed in the behavior of many complex systems of surprisingly different nature. Zipf [l] found a remarkable rank-frequency relationship in linguistics. If we consider a long text and assign ranks to all words that occur in the text in the order of decreasing frequencies, then the frequency f , of a word satisfies the empirical law: f, = cr-p , where c and p are constants and p -1. Zipfs law has been discovered independently in such diverse situations as distribution of biological species, distribution of income, distribution of city populations, etc.[2]