What does the world of Finnegans Wake look like? How do we picture its characters? Most representations are diagrammatic, yet Joyce’s work teems with specific details, objects, and lexical ephemera that are poorly represented by diagrams. This essay proposes the “Arcimboldean” as a starting point. By comparing the unstable characters and spaces of the Wake to the composite style of portraiture associated with the painter Giuseppe Arcimboldo, it raises a number of questions about the nature of Joyce’s world. How are characters composed—both in terms of text and food? How do they relate to Joyce’s characterization in Ulysses? Are they delimitable—or do they, like Joyce’s punning language—overturn authorial control, developing monstrous lives of their own? Arcimboldo can provide not only illustrations but also a critical heuristic: a way of thinking about ontology and order in Finnegans Wake.