with a fixed value $m/L=16$. (a) longitudinal conductivity, (b) transversal conductivity. The lines are provided simply as visual guides.\[fig:scalingp\]](scalingp){width="0.9\linewidth"}

Results {#sec:results}
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Polyominoes formed by discretization
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In practice, the discretization transformed the continuous problem of rods into a lattice problem of linear polyominoes, i.e particles having different shapes and length. The mean number of cells, $k$, in such a polyomino depends on the angle $\theta$ between the axis of the rod and the selected direction, $x$ $$\label{eq:angledistrib}
\frac{k}{k^*} = \frac{1}{k^*} +  \sqrt{2} \sin\left( \theta + \frac{\pi}{4}\right), \quad 0 \leqslant \theta \leqslant \frac{\pi}{4},$$ where $k^* = m/L$ (see Appendix \[app:distribution\] for details).

Figure \[fig:angledistrib\] demonstrates how the size of a polyomino depends on the angle $\theta$. In computer simulation, a rod was randomly placed onto the plane with the angle $\theta = 0$ to the axis $x$ and the size of the generated polyomino was calculated. Then, the rod was turned to an angle equal to $1^\circ$ and the size of the generated polyomino calculated once again. These turns continued until the angle reached $\theta=90^\circ$. After that, the results for each angle were averaged over $10^5$ independent placements of the rods. The dependence obtained by means of this simulation is 