number of occupied cells divided by the total number of cells (i.e., $m^2$) was used to characterize the system after discretization. There is no one-to-one correspondence between the number concentration of rods $n$ and the filling fraction $p$, i.e., one cannot predict the exact value of the packing density even when the number of deposited rods is known.

In all calculations, the quantities under consideration were typically averaged over 100 independent statistical runs for $m\leq256$, over 25 for $m=512$, over 10 for $m=1024$, and over 5 for $m=2048$, unless otherwise explicitly specified in the text.

Scaling analysis {#app:scaling}
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The size of the system was $L\times L$ and, in the present work, all calculations were performed using $L = 32l$. Our choice is based on a scaling analysis. We performed calculation of the electrical conductivities for regions of different sizes $L=16,32,64$. Figure \[fig:scalingp\] compares the results for a fixed value of $k^*$. The differences in the electrical conductivity in the vicinity of zones of the insulator-to-conductor transition were insignificant, and were almost completely absent outside of these regions.

![Example of scaling analysis for electrical conductivity, $\sigma$ vs filling fraction, $p$, for the different values of $L= 16, 32, 64$ but 