A New Class of Cellular Automata for Reaction-Diffusion Systems

We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion, and a probabilistic table-lookup for the reactive part. The applicability of the new CA is demonstrated using the Ginzburg-Landau equation.Comment: 4 pages, RevTeX 3.0 , 3 Figures 214972 bytes tar, compressed, uuencode

Simulating reaction-diffusion cellular automata with JCASim

The program system JCASim is a general-purpose system for simulating cellular automata in Java. It includes a stand-alone application and an applet for web presentations. The cellular automata can be specified in Java, in CDL, or using an interactive dialogue. The system supports many different lattice geometries (1-D, 2-D square, hexagonal, triangular, 3-D), neighborhoods, boundary conditions, and can display the cells using colors, text, or icons. We use three kinds of cellular automata for reaction-diffusion systems to demonstrate the wide applicability of the simulation system. These are microscopic block-CA, reactive lattice gas CA, and macroscopic CA related to finite difference methods

Translations of Cellular Automata for Efficient Simulation

Cellular automata can be described in many di#erent ways, one of which is to use a special purpose description language. Here, the language CDL is used as the source for translations into Java or C code for computer simulations. Several coding styles are generated automatically: The state transition function can be coded as Java code, as C code with stubs for integration into a Java simulation environment, as a lookup table, or as Java code consisting of boolean functions which allow the parallel simulation of 32 or 64 cells on one processor. The coding styles are compared for several examples and it is found that the boolean function style (also called multispin-coding) realized in Java is often, but not always, significantly more e#cient than even native C code

Three-dimensional Cellular Automata for Reaction-Diffusion Systems

Cellular automata for reaction-diffusion systems are efficient enough to make the simulation of large three-dimensional systems feasible. The principal construction mechanisms used here are not much different from those for two-dimensional cellular automata. Diffusion is realized through a local averageing, and all the nonlinear reaction terms are collected in a table-lookup. The special issue in three dimensions is the need to increase time- and spacescales as much as possible to achieve sufficient system sizes. This can be done through the use of numerical integration schemes for constructing the lookup table, and through the use of special diffusion operators. We present examples of complex three-dimensional behaviours in an excitable reaction-diffusion system and in a model of a pattern-forming chemical reaction. 1 Introduction Nonlinear reaction-diffusion systems arise in many different contexts. Examples include the spreading of infectious diseases (e.g., rabies in foxes) or of ..

Coupling Microscopic and Macroscopic Cellular Automata

Cellular automata can model natural phenomena on many different levels of detail. Often, one specific level of detail is appropriate for the problem under investigation. But in some cases a connection between the different levels of detail is necessary. One such case is the catalytic reaction on a surface. The homogeneous crystallographic surface can reasonably well be described by mesoscopic approaches, but in the presence of defects, a microscopic simulation (where each site of the crystal lattice is individually represented) is necessary. In this paper we present a framework for coupling different types of cellular automata to achieve an efficient simulation which is nevertheless detailed enough to resolve microscopic phenomena where necessary. Keywords: Cellular automata, reaction-diffusion systems, coupling, catalytic surface reactions, simulation. Catalytic surface reactions Chemical reactions on a catalytic surface have often been modeled by MonteCarlo methods or cellular aut..