Approach to numerical assessment of the adequacy of a three-dimensional cellular-automaton model of the process of matter diffusion

This paper explores the use of a discrete-dynamic approach, employing three-dimensional cellular automata, to model evolutionary diffusion. The main focus is on verifying the accuracy of modeling classical diffusion using different geometric lattices. We present a numerical technique for assessing the suitability of a cellular automaton algorithm for a test problem: modeling substance diffusion using various threedimensional lattices. Our approach compares the spatiotemporal solution from the finite element method with a discrete cellular automaton solution, identifying the optimal cell geometry that minimizes numerical error. The cellular automaton model is implemented with C# using the Unity platform. Computational experiments investigate the efficiency of the algorithm with different lattices. Error calculations and visualizations indicate that truncated octahedral cellular automata provide the lowest error, making them suitable for discrete-dynamic diffusion modeling. These findings can aid in optimizing cellular automaton model algorithms.