the horizontal, $\sigma_x$ and vertical $\sigma_y$ directions (see [@Lebovka2016; @Lebovka2017] for the detail).

![Transformation of the supporting mesh into a resistor network. All possible combinations of the conductivities are indicated.\[fig:transformation\]](transformation){width="0.9\linewidth"}

The Frank–Lobb algorithm was applied to calculate the electrical conductivity [@Frank1988]. For a quantitative description of the anisotropy of the electrical conductivity in the longitudinal and transversal directions, the electrical conductivity ratio, defined from the electrical contrast $\Delta$, $$\label{eq:deltaxy}
\sigma_y /\sigma_x =\Delta^\delta,$$ was used [@Tarasevich2016]. $\delta=0$ for isotropic systems and $\delta\approx 1$ for highly anisotropic systems with $\sigma_y /\sigma_x \approx \Delta$.

To characterize the insulator–conductor phase transition, we used the mean geometric value $$\label{eq:sigmag}
  \sigma_g =\sqrt{\sigma_m \sigma_p},$$ and treated a system with conductivity $\sigma > \sigma_g$ as conducting, whilst a system with a conductivity $\sigma < \sigma_g$ was considered to be insulating. Note that the mean geometric conductivity corresponds exactly to the prediction for the percolation threshold in the case of 2D systems with equal concentrations of the phases $p_c=1/2$ when both phases are in geometrically equivalent conditions (on average) [@Dykhne1971].

The use of the supporting mesh for the calculation of electrical conductivity is equivalent to the discretization of the structure of the infinitely thin rods and the substitution of 