Variability in cellular automata for modelling substrate diffusion in microbial systems

Computational intensity in large-scale microbial simulations is predominantly associated with resolving substrate advection–diffusion dynamics. The paper develops cellular automata-based techniques for models of substrate diffusion, a discrete framework that offers high computational efficiency and can naturally handle complex geometries. A comparative analysis is conducted for a discrete 2D advection–diffusion model implemented on square, extended-square, and hexagonal cellular automaton lattices. Their accuracy is rigorously verified against reference finite-element solutions. Computational experiments demonstrate that hexagonal-based cellular automata achieve higher accuracy than classical finite-difference-like square lattices, while also enabling more realistic and isotropic simulations in complex microbial systems. This work therefore provides a validated, lattice-specific discretization strategy for diffusion, facilitating its efficient integration into hybrid models of microbial systems.