In this paper the Zipf-Mandelbrot law is revisited in the context of linguistics. Despite its widespread popularity the Zipf–Mandelbrot law can only describe the statistical behaviour of a rather restricted fraction of the total number of words contained in some given corpus. In particular, we focus our attention on the important deviations that become statistically relevant as larger corpora a...

The paper studies the probabilities of the occurrence of m word phrases (m=2,3, ...) in relation with the probabilities of occurrence of the single words. It is well-known that, in the latter case, the law of Zipf is valid (i.e. a power law). We prove that in the case of m word phrases (m22) this is not the case. We present two independent proofs of this. We furthermore show that in case we wan...

This paper illustrates how the Zipf-Mandelbrot law can emerge in language as a result of minimising the cost of categorising sensory images. The categorisation is based on the discrimination game in which sensory stimuli are categorised at different hierarchical layers of increasing density. The discrimination game is embedded in a variant of the language game model, called the selfish game, wh...

We study in depth the equivalence between subshrubs and chaotic bands in the Mandelbrot set. In order to do so, we introduce the rules for chaotic bands and the rules for subshrubs, as well as the transformation rules that allow us to interchange them. From all the denominations of a chaotic band, we show the canonical form; that is, the one associated to the hyperbolic component that generates...

This paper investigates the set of angles of the parameter rays which land on the real slice [−2, 1/4] of the Mandelbrot set. We prove that this set has zero length but Hausdorff dimension 1. We obtain the corresponding results for the tuned images of the real slice. Applications of these estimates in the study of critically non-recurrent real quadratics as well as biaccessible points of quadra...

The study of Mandelbrot Sets (MS) is a promising new approach to the phase transition theory. We suggest two improvements which drastically simplify the construction of MS. They could be used to modify the existing computer programs so that they start building MS properly not only for the simplest families. This allows us to add one more parameter to the base function of MS and demonstrate that...