When faced with the need of implementing a decentralized behavior for a group of collaborating robots, strategies inspired from swarm intelligence often avoid considering the human operator, granting the swarm with full autonomy. However, field missions require at least to share the output of the swarm to the operator. Unfortunately, little is known about the users’ perception of group behavior and dynamics, and there is no clear optimal interaction modality for swarms. In this paper, we focus on the movement of the swarm to convey information to a user: we believe that the interpretation of artificial states based on groups motion can lead to promising natural interaction modalities. We implement a grammar of decentralized control algorithms to explore their expressivity. We define the expressivity of a movement as a metric to measure how natural, readable, or easily understandable it may appear. We then correlate expressivity with the control parameters for the distributed behavior of the swarm. A first user study confirms the relationship between inter-robot distance, temporal and spatial synchronicity, and the perceived expressivity of the robotic system. We follow up with a small group of users tasked with the design of expressive motion sequences to convey internal states using our grammar of algorithms. We comment on their design choices and we assess the interpretation performance by a larger group of users. We show that some of the internal states were perceived as designed and discuss the parameters influencing the performance.