Fractal paradigm of water-as-motion: Indeterminate being, decentred voluminosity, and orderly chaos

This article develops a fractal paradigm of water as an ontological and analytical framework for rethinking water beyond the modernist conception of H 2 O as an atomistic and ontologically determinate substance. Drawing on the philosophy of movement and new materialist thought which critique ontological atomism and instead emphasise motion, change, and indeterminacy, the article proposes understanding water primarily through its fractal motion: water-as-motion . Building on the mathematical origins of fractals and their grounding in water-related forms (such as waves, turbulence, coastlines, and river meanders), the article expands the notion of the fractal into a broader conceptual paradigm for philosophies and geographies of water – one that arises from water's own materiality rather than being imposed upon it. The paper develops four “fractal curves” as conceptual openings. First, it argues that fractal water redirects analysis toward decentered scalar voluminosity , bridging debates on non-hierarchical scaling and decentered ontologies by showing how water emerges through intra-scalar, self-similar motion. Second, it conceptualises relationality as immanent to an ontology of motion and change: water-as-motion is relational to itself, but also to other matter and life forms, through continuous and collective transformation. Third, it rethinks order and efficiency through the notion of orderly chaos : a form of biophysical order that emerges not from linear causality but from indeterminate, yet metastable self-organisation. Finally, it frames fractal repetition as a source of vitality, suggesting that water's finite materiality becomes life-generative through the temporal and spatial cycles of fractal repetition.