Grid anisotropy of propagation fronts in cellular automata and its reduction methods

Abstract

Cellular Automata (CA) is a qualitative simulation method widely used in complex systems. However, the anisotropy of the bottom grid is influenced by the sharp boundary, which leads to the problem of grid-induced anisotropy. It not only makes the CA show the anisotropy in the simulation of isotropic propagation, but also produces errors in the simulation of anisotropic propagation. Through a simple binary CA simulation, this paper discusses reasons and processes of grid anisotropy from three aspects: cellular space, neighbor rules and evolution rules, and the error between CA simulation and standard circle propagation is evaluated. Afterwards, five methods for reducing grid anisotropy are introduced and compared in isotropic and anisotropy propagation simulation. For illustration purpose, these methods are considered in the actual system of isotropic and anisotropic propagation, and then the CA model is successfully applied to the classical isotropic propagation, i.e. the chemical wave in B-Z reaction-diffusion system, and classical anisotropic propagation, i.e. the dendritic growth in crystallization system. The results show that the composition shape of neighboring cells affects the isotropic propagation process of CA simulation, and the square grid is one of potential upgrading methods. The weight of neighbors algorithm is more suitable for simulating diffusion processes, and the limited circular neighbourhood algorithm is more suitable for crystal growth process. These results can be a reference for quantitative application of CA in fields of chemical wave propagation and dendrite growth.