  The fragmentation processes of exchangeable partitions have already been
studied by several authors. In this paper, we examine rather fragmentation of
exchangeable compositions, that means partitions of $\mathbb{N}$ where the
order of the blocks counts. We will prove that such a fragmentation is
bijectively associated to an interval fragmentation. Using this correspondence,
we then calculate the Hausdorff dimension of certain random closed set that
arise in interval fragmentations and we study Ruelle's interval fragmentation.
