The motivation of this paper is to highlight the importance of visual representations for artists when modeling and simulating mass-interaction physical networks in the context of sound synthesis and musical composition. GENESIS is a musician-oriented software environment for sound synthesis and musical composition. However, despite this orientation, a substantial amount of effort has been put into building a rich variety of tools based on static or dynamic visual representations of models and of abstractions of their properties. After a quick survey of these tools, we will illustrate the significant role they play in the creative process involved when going from a musical idea and exploration to the production of a complete musical piece. To that aim, our analysis will rely on the work and practice of several artists having used GENESIS in various ways.