Gille Deleuze’s fundamental contributions to the field of cinematography put an end, within the structuralism, to the long discussion about the possibility to analyze the audiovisual mechanisms of creation of meaning through the instruments of linguistics. In fact, in Cinéma 1 and Cinéma 2, Deleuze posits that within the audiovisual field narrative is a pure spatial organization, and that, as a consequence, any reference to the linguistic model should have been avoided. By distancing himself from both linguistic terminology and approaches - e.g. by distancing himself from the so-called cinematic rhetorical figures - Deleuze’s analysis sheds light not only on the geometrical character of the audiovisual narrative but also on its non-Euclidean nature. By considering Bresson’s narrative spaces as Rimannian spaces, and those of Resais as topological spaces, Deleuze developed a new analytical instrument able at examining the digital images, now considered a composite image and, therefore, a non-Euclidean image by nature. Through the concepts of non-Euclidean geometries, this paper deals with the narrative phenomenon derived from the introduction of ‘new gazes’, those produced by the use and popularization of new technologies. The paper proposes, indeed, through the notion of gaze, an analysis of the relation between the database and the interface, previously called, under the influence of structuralism, paradigm and syntagm respectively. Taking as starting points the concepts of topology and fractal geometry, the text will also deal with some narrative phenomena that arose when video-electronic, and then digital technology, became popular and started to take an active part within the creative process. This survey will allow to better comprehend the non-Euclidean composition and, therefore, the multidimensional (2D, 3D, 5D, Mixed Reality, among others) audiovisual narrative spaces, that is spaces able at creating hypertextual networks in which different mechanism of production of meaning that formerly belonged to other media converge and merge.