Recent work in experimental semiotics has started to investigate the cognitive processes supporting the emergence of human communicative systems. We present a computational model of the cognitive processes involved in establishing a novel referential communicative system, as operationalized with the Tacit Communication Game (TCG). This experimental paradigm has been used to study the socio-cognitive underpinnings of human communication. We model how players of the TCG can successfully generate and understand communicative behavior in a novel, visuospatial domain using Structure Mapping Theory (SMT). Many of the processes necessary to communicate in this game are forms of analogical reasoning that are captured by SMT (e.g. abstraction and analogical transfer). Yet, we also identify cognitive processes—not yet formalized under SMT—that are necessary for the genesis of new communicative systems. This is an important first step in formally characterizing this creative socio-cognitive ability.