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In this paper we consider statistical estimates of threshold and strength of percolation clusters on square lattices. The percolation threshold p_c and the strength of percolation clusters P_∞ for a square lattice with (1,π)-neighborhood depends not only on the lattice dimension, but also on the Minkowski exponent d. To estimate the strength of percolation clusters P_∞ proposed a new method of averaging the relative frequencies of the target subset of lattice sites. The implementation of this method is based on the SPSL package, released under GNU GPL-3 using the free programming language R.

In this paper we consider various models of hydraulic hysteresis in invasive mercury porosimetry. For simulating the hydraulic hysteresis is used isotropic site percolation on three-dimensional square lattices with $(1,\,\pi)$-neighborhood. The relationship between the percolation model parameters and invasive porosimetry data is studied phenomenologically. The implementation of the percolation model is based on libraries SPSL and SECP, released under license GNU GPL-3 using the free programming language R.

This paper examines the impact of the spatial resolution of a discretized (lattice) representation of the environment on the efficiency and correctness of optimal pathfinding in complex environments. Scenarios are considered that may include bottlenecks, non-uniform obstacle distributions, and areas of increased safety requirements in the immediate vicinity of obstacles. Despite the widespread use of lattice representations of the environment in robotics due to their compatibility with sensor data and support for classical trajectory planning algorithms, the resolution of these lattices has a significant impact on both goal reachability and optimal path performance. An algorithm is proposed that combines environmental connectivity analysis, trajectory optimization, and geometric safety refinement. In the first stage, the Leath algorithm is used to estimate the reachability of the target point by identifying a connected component containing the starting position. Upon confirmation of the target point’s reachability, the A* algorithm is applied to the nodes of this component in the second stage to construct a path that simultaneously minimizes both the path length and the risk of collision. In the third stage, a refined obstacle distance estimate is performed for nodes located in safety zones using a combination of the Gilbert – Johnson –Keerthi (GJK) and expanding polyhedron (EPA) algorithms. Experimental analysis revealed a nonlinear relationship between the probability of the existence and effectiveness of an optimal path and the lattice parameters. Specifically, reducing the spatial resolution of the lattice increases the likelihood of connectivity loss and target unreachability, while increasing its spatial resolution increases computational complexity without a proportional improvement in the optimal path’s performance.

In this paper we consider the structure of site percolation models on three-dimensional square lattices with various shapes of (1,π)-neighborhood. For these models, are proposed iso- and anisotropic modifications of the invasion percolation algorithm with (1,0)- and (1,π)-neighborhoods. All the above algorithms are special cases of the anisotropic invasion percolation algorithm on the n-dimensional lattice with a (1,π)-neighborhood. This algorithm is the basis for the package SPSL, released under GNU GPL-3 using the free programming language R.