  We are interested in connections between the theory of fractal sets obtained
as attractors of iterated function systems and process calculi. To this end, we
reinterpret Milner's expressions for processes as contraction operators on a
complete metric space. When the space is, for example, the plane, the
denotations of fixed point terms correspond to familiar fractal sets. We give a
sound and complete axiomatization of fractal equivalence, the congruence on
terms consisting of pairs that construct identical self-similar sets in all
interpretations. We further make connections to labelled Markov chains and to
invariant measures. In all of this work, we use important results from process
calculi. For example, we use Rabinovich's completeness theorem for trace
equivalence in our own completeness theorem. In addition to our results, we
also raise several questions related to both fractals and process calculi.
