Persistence of the linguistic categories.

<p>(a) The rescaled average number of linguistic categories versus the rescaled number of games for three different population sizes (, and ). The plateau behaviour for the average number of linguistic categories is collapsed by rescaling the ordinate by and the abscissa by . The inset shows the data collapse for the first part of the evolution where the ordinate is rescaled by and the abscissa by . (b) The rescaled persistence time of (i.e., the time spent by the system in a configuration corresponding to an average of linguistic categories) versus the rescaled for , and (legends correspond to those in (a) except that the curves are plotted with both lines and symbols here). Once again the ordinate is rescaled by and the abscissa by for data collapse. The inset shows a zoomed and uncollapsed version of the data (indicating the need for the collapse). Here the value of is set to the average human JND <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0016677#pone.0016677-Long1" target="_blank">[38]</a>.</p

Typical long-time configuration of five representative agents in the population.

<p>For each agent perceptual and linguistic categories (separated by short and long bars, respectively) are shown. The highlighted portion of two agents illustrates an instance of a successful game in a so-called mismatch region between the linguistic categories of the two agents associated with the words “a” and “b” (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0016677#s4" target="_blank">Materials and Methods</a> for details). The hearer - in a previous game - learned the word “a” as a synonym for the perceptual category at the leftmost boundary of the linguistic category “b”. During the game the speaker utters “a” for the topic; as a result the hearer deletes “b” from her inventory, keeping “a” as the name for that perceptual category, moving <i>de facto</i> the linguistic boundary.</p

Finite-size effects.

<p>The rescaled average number of linguistic categories versus the rescaled number of games for five different population sizes (, , , and ). The bending region of the curves is collapsed by rescaling the number of linguistic categories by and the time axis as where , , and . The inset shows a zoomed version of the same plot to present a better visualization of the data collapse.</p

Words per perceptual category.

<p>The average number of words per perceptual category across the population of  = 300, 500 agents versus the number of games per player. The inset is a zoom showing after games per player. Clearly, does not settle to one even after a very long time. The value of here is equal to which is the average of human JND (when projected on the interval) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0016677#pone.0016677-Long1" target="_blank">[38]</a>.</p

Linguistic vs. perceptual categories.

<p>Parametric plot of the number of linguistic categories vs. the number of perceptual categories, , for different population sizes for which the bending region is accessible within a reasonable time (, and ). It is evident that there is a transition (indicated by the bold arrow) between a long-lasting regime where the number of perceptual categories keeps increasing, though at a very slow pace, and a regime where discrimination stops, the number of perceptual categories does not increase anymore and one observes only a decrease in the number of linguistic categories. The inset shows one representative example of the time evolution of and for  = 100 where the bold arrow marks the onset of the bending.</p