  Multiple resolution analysis of two dimensional structures composed of
randomly adsorbed penetrable rods, for densities below the percolation
threshold, has been carried out using box-counting functions. It is found that
at relevant resolutions, for box-sizes, $r$, between cutoffs given by the
average rod length $<\ell>$ and the average inter-rod distance $r_1$, these
systems exhibit apparent fractal behavior. It is shown that unlike the case of
randomly distributed isotropic objects, the upper cutoff $r_1$ is not only a
function of the coverage but also depends on the excluded volume, averaged over
the orientational distribution. Moreover, the apparent fractal dimension also
depends on the orientational distributions of the rods and decreases as it
becomes more anisotropic. For box sizes smaller than $<\ell>$ the box counting
function is determined by the internal structure of the rods, whether simple or
itself fractal. Two examples are considered - one of regular rods of one
dimensional structure and rods which are trimmed into a Cantor set structure
which are fractals themselves. The models examined are relevant to adsorption
of linear molecules and fibers, liquid crystals, stress induced fractures and
edge imperfections in metal catalysts. We thus obtain a distinction between two
ranges of length scales: $r < <\ell>$ where the internal structure of the
adsorbed objects is probed, and $<\ell> < r < r_1$ where their distribution is
probed, both of which may exhibit fractal behavior. This distinction is
relevant to the large class of systems which exhibit aggregation of a finite
density of fractal-like clusters, which includes surface growth in molecular
beam epitaxy and diffusion-limited-cluster-cluster-aggregation models.
