Fig. 4.

Empirical rank distribution of word frequencies in The Origin of Species (black), showing two power-law regimes. For the most frequent words, the distribution is approximately power-law with an exponent $\gamma \sim 0.9$. The corresponding distribution for the ${\Phi }^{\left(\lambda \right)}$ process with $\lambda =0.9$ (red), suggests a slight deviation from perfect nesting. This means that in sentence formation, about 90% of consecutive word pairs, sample space is strictly reducing. Simulation: $N=\mathrm{5,000}$ (words), and $M=\mathrm{10,000}$ restarts (sentences).