The regions associated with high levels of vorticity and energy dissipation are studied in numerically simulated isotropic turbulence at $Re_\lambda = 168$. Their geometry and spatial distribution are characterized by means of box-counting methods. No clear scaling is observed for the box counts of intense strain rate and vorticity sets, presumably due to the limited inertial range, but it is shown that, even in that case, the box-counting method can be refined to characterize the shape of the intense structures themselves, as well as their spatial distribution. The fractal dimension of the individual vorticity structures, $D_\omega \rightarrow 1.1 \pm 0.1$, suggests that they tend to form filamentary vortices in the limit of high vorticity threshold. On the other hand, the intense dissipation structures have dimensions $D_{s} \simeq 1.7 \pm 0.1$, with no noticeable dependence on the threshold, suggesting structures in the form of sheets or ribbons. Statistics of the associated aspect ratios for different thresholds support these observations. Finally box counting is used to characterize the spatial distribution of the baricentres of the structures. It is found that the intense structures are not randomly distributed in space, but rather form clusters of inertial-range extent, implying a large-scale organization of the small-scale intermittent structures.