Oceanic turbulence has been considered for a while as one of the main sources of the heterogeneity of the phytoplankton field over a wide range of scales. However, it is only recently that the intermittency of turbulence has been taken into account, although it is rather indispensable in the explanation of the observed patchiness of the plankton field. In order to improve the understanding and characterization of the diffusion of copepods within an heterogeneous phytoplankton field, we developed a model based on particle diffusion in a multifractal field. After discussing this model with some detail, we used it and the corresponding numerical simulations in order to investigate the fundamental question: does the strong heterogeneity of the phytoplankton generate a anomalous diffusion of the copepods? Although a positive answer is obtained in a rather straightforward manner for a one-dimensional multifractal field of phytoplankton concentration, the answer is rather more involved for a greater (topological) dimension of the field, contrary to some previous claims.