In this chapter, a framework for assessing the openness of virtual archaeological reconstructions to a multiplicity of readings is presented by focusing on the case of Çatalhöyük, in Turkey. Since its discovery in the 1950s, there has been a diversity of opinion on Çatalhöyük’s settlement rank along the path from settled village to urban agglomeration. This diversity of opinion has been expressed both verbally and visually, the latter including numerous computer-based visualizations for a variety of purposes and target audiences. Among the internationally approved principles for computer-based visualizations of cultural heritage is the need for intellectual and scientific transparency. Umberto Eco’s theory of the “open work,” as applied in literary and visual works including motion pictures, offers a theoretical framework for discussing the transparency of Çatalhöyük visualizations, as does Siegfried Kracauer’s idea of “cinematic materiality.” Three of the virtual works on Çatalhöyük are briefly presented in this chapter, as a basis for discussing the applicability of Eco’s and Kracauer’s ideas in this type of production as a measure for “open multivocality,” leading to an assessment of whether visualizations reveal any or all alternative interpretations of the site.