Multi-scale Modeling with Cellular Automata: The Complex Automata Approach

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.

[1]  Philip K. Maini,et al.  The Use of Hybrid Cellular Automaton Models for Improving Cancer Therapy , 2004, ACRI.

[2]  Bastien Chopard,et al.  Cellular Automata Modeling of Physical Systems: Index , 1998 .

[3]  E. F. Codd,et al.  Cellular automata , 1968 .

[4]  Daniel M. Tartakovsky,et al.  Guest Editors' Introduction: Multiphysics Modeling , 2005, Comput. Sci. Eng..

[5]  Peter M. A. Sloot,et al.  Computational e-Science: Studying complex systems in silico. A National Coordinated Initiative. White Paper. , 2007 .

[6]  Alfons G. Hoekstra,et al.  Error Investigations in Complex Automata Models for Reaction-Diffusion Systems , 2008, ACRI.

[7]  Andreas Deutsch,et al.  Cellular Automaton Modeling of Biological Pattern Formation - Characterization, Applications, and Analysis , 2005, Modeling and simulation in science, engineering and technology.

[8]  Peter M. A. Sloot,et al.  Modeling Dynamic Systems with Cellular Automata , 2007, Handbook of Dynamic System Modeling.

[9]  Alfons G. Hoekstra,et al.  Scale-Splitting Error in Complex Automata Models for Reaction-Diffusion Systems , 2008, ICCS.

[10]  Nils A. Baas,et al.  Higher Order Cellular Automata , 2005, Adv. Complex Syst..

[11]  K. Zuse,et al.  The computing universe , 1982 .

[12]  Jörg R. Weimar Coupling microscopic and macroscopic cellular automata , 2001, Parallel Comput..

[13]  Navot Israeli,et al.  Computational irreducibility and the predictability of complex physical systems. , 2003, Physical review letters.

[14]  Jack Dongarra,et al.  Computational Science - ICCS 2007, 7th International Conference, Beijing, China, May 27 - 30, 2007, Proceedings, Part III , 2007, ICCS.

[15]  Hartmut Bossel,et al.  Modeling and simulation , 1994 .

[16]  Alfons G. Hoekstra,et al.  Toward a Complex Automata Formalism for Multi-Scale Modeling , 2007 .

[17]  Konrad Zuse,et al.  Rechnender Raum , 1991, Physik und Informatik.

[18]  Roger White Modeling Multi-scale Processes in a Cellular Automata Framework , 2006 .

[19]  S. Lloyd Computational capacity of the universe. , 2001, Physical review letters.

[20]  E Weinan,et al.  Heterogeneous multiscale methods: A review , 2007 .

[21]  Lin,et al.  Lattice boltzmann method on composite grids , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  David A. Bader Petascale Computing: Algorithms and Applications , 2007 .

[23]  Bastien Chopard,et al.  Cellular Automata Modeling of Physical Systems , 1999, Encyclopedia of Complexity and Systems Science.

[24]  Marian Bubak,et al.  Towards Distributed Petascale Computing , 2007, ArXiv.

[25]  Alfons G. Hoekstra,et al.  Towards a Complex Automata Framework for Multi-scale Modeling: Formalism and the Scale Separation Map , 2007, International Conference on Computational Science.

[26]  Yûval Pôrṭûgālî Complex artificial environments : simulation, cognition and VR in the study and planning of cities , 2006 .

[27]  B. Chopard,et al.  Theory and applications of an alternative lattice Boltzmann grid refinement algorithm. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.