The magnetic turbulence in the solar wind causes a magnetic field line transport that is reflected in the propagation in space of charged particles. Assuming a small localized source, the distribution in space of energetic particles is determined, in part, by the shape of the magnetic flux tube. The spatial evolution of a magnetic flux tube is studied here by means of a numerical realization of three-dimensional magnetic turbulence that takes into account the anisotropy of the solar wind turbulence and is quantified by correlation lengths in the three spatial directions. Several diagnostics of flux tube evolution are shown, such as patterns of the flux tube cross sections and histograms representing possible energetic particle intensity profiles. We show that flux tube evolution can be assessed by the Kubo number R = (δB/B0)(lz/lx), where δB/B0 is the turbulence level and lz (lx) is the correlation length parallel (transversal) to the background magnetic field B0. We find that when lz/lx (i.e., R) is large, the flux tube evolves very quickly, forming very fine, diffusive structures. These diffusive structures would correspond to a nearly Gaussian envelope for the energetic particle time profile detected by a spacecraft. On the other hand, when lz/lx is small, the flux tube evolves slowly, executing large coherent transverse displacements, and thereby forms well resolved (i.e., detached) intermittent high particle fluxes in observed energetic particle profiles. Hence an accurate study of the morphology of impulsive energetic particle events, when compared with our simulation results, can give information on the microphysical evolution of flux tubes in the solar wind and on the turbulence anisotropy. A first comparison indicates that lx ≃ 3--10lz is appropriate for the solar wind. Our study also allows us to reconcile fast field line transport with the observation of sharp composition or energetic particle gradients in the solar wind, since lx ≫ lz implies considerable transverse elongation of the flux tube cross section, with the possibility of non-Gaussian, superdiffusive transport regimes.