Diffusion-weighted (DW) magnetic resonance imaging is the only non-invasive and in-vivo method available for studying brain white matter anatomical connectivity. Tractography algorithms have been developed to reconstruct neuronal tracts utilizing DW images. In this study, a new tractography method is presented. This is based on a fuzzy framework, as suggested by the intrinsic fuzzy nature of medical images. The proposed technique checks all possible paths -defined on the discrete image grid- between any pair of voxels and assigns a connectivity value, representative of the strength of the strongest path. Path branching, which is not well captured by binary streamline techniques, is inherently considered. Compared to other distributed tractography approaches, our method combines a) converged connectivity values for all image voxels, b) connectivities that do not drop systematically with the distance from the seed, c) path propagation with relatively high angular resolution and d) fast execution times. Results are shown on both simulated and real images, where predicted tracts agree well with a-priori anatomical knowledge.