and dispersity of the polyominoes could not be eliminated even at infinitely fine discretization. For example, for a disordered system ($s=0$) the estimated critical number density for the polyominoes $n_c^i \approx 6$ was greater than that for zero-width rods, $n_c^i =5.6372858(6)$ [@Mertens2012]. Alignment of the fillers could result in noticeable electrical anisotropy. The electrical properties of the films with perfectly aligned rods ($s = 1$) were different from that for slightly disordered systems ($0.6< s < 1$). For a perfectly aligned system, the highest film anisotropy was observed at high filler content ($p \approx 0.55$) for essentially non-transparent films. For non-perfectly aligned systems, high electrical anisotropy was observed at smaller filler content and this suggests a potential method for the production of optically transparent and highly anisotropic conducting films.

We acknowledge funding provided by the National Academy of Sciences of Ukraine, Project No. 43/18-H and 15F (0117U006352) (N.I.L. and N.V.V.) and the Ministry of Education and Science of the Russian Federation, Project No. 3.959.2017/4.6 (Yu.Yu.T., A.V.E., and R.K.A.). The authors would like to thank V.V. Chirkova for her technical assistance.

Size distribution of polyominoes {#app:distribution}
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Let there be a line segment (a rod) of length $l$, which is randomly 