Cellular automaton model of three-dimensional excitable media

A ‘third generation’ cellular automaton (CA) model of excitable media, introduced in 1992 by Weimar, Tyson and Watson (Physica D, 1992, 55, 309; 328) is extended to three spatial dimensions (3D). Diffusion is described by 3D Gaussian masks and the update rules are devised to mimic the FitzHugh–Nagumo partial differential equations (PDEs) of excitability. The CA is intended to explore the properties of rotating scroll waves. 3D domains of several λ3(λ= wavelength of scroll) can be simulated by the CA on a typical desktop workstation, and larger domains are suitable for parallel processing by methods described. The accuracy and performance of the CA, as a simulation tool for continuous excitable media, are assessed by comparing CA and PDE results for scroll waves of various geometries and parameters.