Spreadable cellular automata: modelling and simulations

The spreadable phenomena which describes the expansion in time of a given spatial property has been studied using models based on partial differential equations. These spreadable dynamics are generally non-linear and then difficult to simulate particularly in two dimensions. In this article, we propose cellular automata (CA) models as an alternative modelling tool that can easily simulate spreadable systems. CA are capable of describing complex systems based on simple evolution rules, which provide numerical schemes directly implemented on computers without approximation or rounding errors. We design local CA dynamics which allow us to maintain a spatial property on non-decreasing subdomains. Several numerical results are performed to illustrate spreadable phenomena. The simulation results corroborate the general shape theory that exhibits the convergence to a specific domain independently on initial conditions.