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The research was supported by the subsidy of the Ministry of Education and Science (Poland) for the Lublin University of Technology as funds allocated for scientific activities in the scientific discipline of Automation, Electronics, Electrical Engineering and Space Technologies—grants: FD-20/EE-2/701, FD-20/EE-2/702, FD-20/EE-2/705, FD-20/EE-2/707.
In this study, an in-depth analysis of the percolation phenomenon for square matrices with
dimensions from L = 50 to 600 for a sample number of 5 × 104 was performed using Monte Carlo
computer simulations. The percolation threshold value was defined as the number of conductive
nodes remaining in the matrix before drawing the node interrupting the last percolation channel,
in connection with the overall count of nodes within the matrix. The distributions of percolation
threshold values were found to be normal distributions. The dependencies of the expected value
(mean) of the percolation threshold and the standard deviation of the dimensions of the matrix were
determined. It was established that the standard deviation decreased with the increase in matrix
dimensions, ranging from 0.0262253 for a matrix with L = 50 to 0.0044160 for L = 600, which is
almost six-fold lower. The mean value of the percolation threshold was practically constant and
amounted to approximately 0.5927. The analysis involved not only the spatial distributions of
nodes interrupting the percolation channels but also the overall patterns of node interruption in the
matrix. The distributions revealed an edge phenomenon within the matrices, characterized by the
maximum concentration of nodes interrupting the final percolation channel occurring at the center
of the matrix. As they approached the edge of the matrix, their concentration decreased. It was
established that increasing the dimensions of the matrix slowed down the rate of decrease in the
number of nodes towards the edge. In doing so, the area in which values close to the maximum
occurred was expanded. Based on the approximation of the experimental results, formulas were
determined describing the spatial distributions of the nodes interrupting the last percolation channel
and the values of the standard deviation from the matrix dimensions. The relationships obtained
showed that with increasing matrix dimensions, the edge phenomenon should gradually disapp
