CELLULAR-AUTOMATON MODEL OF 3-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 d escribed by 3D Gaussian masks and the update rules are devised to mimi c the FitzHugh-Nagumo partial differential equations (PDEs) of excitab ility. The CA is intended to explore the properties of rotating scroll waves. 3D domains of several lambda(3) (lambda = wavelength of scroll ) can be simulated by the CA on a typical desktop workstation, and lar ger domains are suitable for parallel processing by methods described. The accuracy and performance of the CA, as a simulation tool for cont inuous excitable media: are assessed by comparing CA and PDE results f or scroll waves of various geometries and parameters.