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Cellular Automata are commonly used to describe complex natural phenomena. In many cases it is required to capture the multi-scale nature of these phenomena. A single Cellular Automata model may not be able to efficiently simulate a wide range of spatial and temporal scales. It is our goal to establish a Cellular Automata modeling paradigm for multi-scale processes. Here we will demonstrate that Complex Automata, a paradigm that we recently introduced, are capable to facilitate such modeling.

We consider two formulations of a cellular automata: the first one uses a gather-update paradigm and the second one a collision-propagation paradigm. We show the equivalence of both descriptions and, using the latter paradigm, we propose a simple way to define a Cellular Automata on a graph with arbitrary topology. Finally, we exploit the duality of formulation to reconsider the problem of characterizing invertible cellular automata.

Mechanisms of endowing cellular automata (CA) models with anticipation property are considered. As a background for investigation a widely known Conway's game of `Life' was chosen. Even within this simple model, introduction of anticipation has a crucial impact on the behavior of the system, resulting in emergence of multiple co-existing solutions. The inherent behavioral templates of classical `Life' (fixed point, cycle, chaos) are valid for its anticipatory version; however, they develop at a level of sets of configurations. Extensive computational simulations were held and the most eloquent results are presented.

Complex Automata (CxA) have been recently introduced as a paradigm to simulate multiscale systems as a collection of generalized Cellular Automata on different scales. We present a basic mathematical framework to investigate the behavior of a CxA model depending on scale separation and modeling choices. In particular, a simple CxA model for a reaction-diffusion system, based on the lattice Boltzmann method, will be formally analyzed. Theoretical error estimates will be derived and numerically validated.

The present paper deals with flow simulations of granular materials moving inside container using Cellular Automata (CA). CA is a class of computer modeling techniques, which consists of discrete unit elements arranged uniformly on spaces, each of which can vary within a finite set of values to express the physical state of the components of the system. The time of evolution of the element state is performed synchronously according to local neighbor rules, instead of governing equations, taking into account the state of the element itself and its nearby elements. Compared with the conventional method such as DEM, it is addressed that the modeling techniques with CA provide advantages on the point of computation efficiency and numerical stability due to the discrete treatment of time and space. In this study, the damping characteristics of a granular damper is investigated numerically by Cellular Automata model and also by DEM, where a container which incorporates granular materials is attached to the mass of one-DOF vibrating system. The container is treated two-dimensionally with thickness identical to a diameter of particle. The simulated particle motions and the damping effects obtained by CA model is compared with DEM solution as well as experimental results, and the present CA model is evaluated in qualitative aspects.

This paper presents a research in the context of pedestrian dynamics according to Situated Cellular Agent (SCA), a Multi-Agent Systems approach whose roots are on Cellular Automata (CA). The aim of this work is to apply Genetic Programming (GP) approach, a well known Machine Learning method belonging to the family of Evolutionary Algorithms, to generate suitable behavioral rules for pedestrians in an evacuation scenario. The main contribution of this work is in the design of a testset of GP generated behaviors to represent basic behavioral models of evacuees populating a only locally known environment, a typical scenario for CA-based models. © 2008 Springer-Verlag Berlin Heidelberg.

Deciphering the influence of the interaction among the constituents of a complex system on the overall behaviour is one of the main goals of complex systems science. The model we present in this work is a 2D square cellular automaton whose of each cell is occupied by a complete random Boolean network. Random Boolean networks are a well-known simplified model of genetic regulatory networks and this model of interacting RBNs may be therefore regarded as a simplified model of a tissue or a monoclonal colony. The mechanism of cell-to-cell interaction is here simulated letting some nodes of a particular network being influenced by the state of some nodes belonging to its neighbouring cells. One possible means to investigate the overall dynamics of a complex system is studying its response to perturbations. Our analyses follow this methodological approach. Even though the dynamics of the system is far from trivial we could show in a clear way how the interaction affects the dynamics and the global degree of order. © 2008 Springer-Verlag Berlin Heidelberg.