Dynamics of a Cellular Automaton with Randomly Distributed Elements
Mario Markus · 2020
This chapter presents a novel theoretical approach to the simulation of excitable media with cellular automata. Using spatially randomized elements, this approach solves the long-lasting problem of anisotropic wave propagation. As an efficient alternative to partial differential equations, simulations of excitable media have been performed using cellular automata. Waves rotating around a hole were actually the first waves in an excitable medium simulated with a cellular automaton. These historical simulations were intended to mimic rotating waves during heart arrhythmias. The problem of anisotropic cellular automata is also encountered in fluid dynamics. In fact, the HPP model, which uses square cells, is highly anisotropic. The automata with extended neighborhood yields waves that are not polygonal as in the automata presented previously but have more-or-less rounded corners, the degree of isotropy depending on the model parameters. The goal of the present work is to solve the anisotropy problem for realistic automata simulations of excitable media.