From classical infinite space–time CA to a hybrid CA model for natural sciences modeling

Complex phenomena occurring in natural sciences are usually characterized by a non trivial interplay between microscopic and macroscopic dynamics, which can be successfully captured by the cellular automata (CA) computational paradigm. In this paper we show that some approximation of the classical CA paradigm is needed in order to properly deal with complex dynamical systems. Real phenomena can be efficiently modeled and simulated by introducing a modified CA approach, the CANv2. In this way one takes into account multiscale dynamics, through approximate infinite and/or infinitesimal dynamical stages, by means of a hybrid network of standard CA components and global operators. The power of the CANv2 approach is fully exploited by discussing three examples borrowed from the realm of natural science: debris flows after a landslide, superconductive devices and forest fires spread. Advantages and limitations of our computational model explicitly arise when examples are discussed.