We forge 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 many questions related to both fractals and process calculi.

翻译：本文建立了由迭代函数系统吸引子获得的分形集理论与进程演算之间的联系。为此，我们将米尔纳的进程表达式重新解释为完备度量空间上的压缩算子。当该空间为平面时，不动点项的指称对应于常见的分形集。我们给出了分形等价的一个可靠且完备的公理化系统，该等价关系是项上的同余关系，由在所有解释中构造相同自相似集的项对组成。我们进一步建立了与带标签马尔可夫链及不变测度的联系。在整个工作中，我们运用了进程演算中的重要成果。例如，在我们自身的完备性定理中，我们使用了拉比诺维奇关于迹等价的完备性定理。除了我们的结果，我们还提出了许多与分形和进程演算相关的问题。