  We investigate an opinion model consisting of a large group of interacting
agents, whose opinions are represented as numbers in $[-1,1]$. At each update
time, two random agents are selected, and the opinion of the first agent is
updated based on the opinion of the second (the ``persuader''). We derive the
mean-field kinetic equation describing the large population limit of the model,
and we provide several quantitative results establishing convergence to the
unique equilibrium distribution. Surprisingly, in some range of the model
parameters, the support of the equilibrium distribution exhibits a fractal
structure. This provides a new mathematical description for the so-called
opinion fragmentation phenomenon.
