  In this article, starting from a Gibbs capacity, we build a new random
capacity by applying two simple operators, the first one introducing some
redundancy and the second one performing a random sampling. Depending on the
values of the two parameters ruling the redundancy and the sampling, the new
capacity has very different multifractal behaviors. In particular, the
multifractal spectrum of the capacity may contain two to four phase
transitions, and the multifractal formalism may hold only on a strict subset
(sometimes, reduced to a single point) of the spectrum's domain.
