This paper explores the application of fractal geometry, specifically fractal dimensions, to the quantitative analysis of Paleolithic parietal art. Traditionally studied through qualitative art historical or archaeological lenses, ancient cave paintings and engravings exhibit complex, irregular, and self-similar patterns characteristic of fractal objects. By employing methods such as the box-counting algorithm, we aim to quantify the inherent complexity and dimensionality of various motifs, styles, and superimpositions found in prominent Paleolithic sites. The study proposes a methodology for digitizing high-resolution images of parietal art, preprocessing them, and calculating their fractal dimensions. Hypothetical results suggest variations in fractal dimensions between different artistic traditions, chronological periods, or even individual artists, reflecting distinct cognitive approaches to representation and pattern generation. The discussion considers the implications of these findings for understanding the perceptual and cognitive processes of Upper Paleolithic humans, their aesthetic principles, and the potential for a new, objective metric in archaeological art analysis. This interdisciplinary approach offers a novel perspective on the structural properties of prehistoric art, providing a quantitative framework to complement existing qualitative interpretations and fostering a deeper understanding of our earliest artistic expressions.