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We present an interactive texture-based algorithm for visualizing three-dimensional steady and unsteady vector fields. The goal of the algorithm is to provide a general volume rendering framework allowing the user to compute three-dimensional flow textures interactively and to modify the appearance of the visualization on the fly. To achieve our goal, we decouple the visualization pipeline into two disjoint stages. First, flow lines are generated from the 3D vector data. Various geometric properties of the flow paths are extracted and converted into a volumetric form using a hardware-assisted slice sweeping algorithm. In the second phase of the algorithm, the attributes stored in the volume are used as texture coordinates to look up an appearance texture to generate both informative and aesthetic representations of the vector field. Our algorithm allows the user to interactively navigate through different regions of interest in the underlying field and experiment with various appearance textures. With our algorithm, visualizations with enhanced structural perception using various visual cues can be rendered in real time. A myriad of existing geometry-based and texture-based visualization techniques can also be emulated.